Check this list of universities. When I graduated, no one told me that I still had Alumni Access to JSTOR provided by my school, and I only found this out several years later. There are about 100 schools that do apparently.

Edit: In the best /r/AskHistorians tradition, the dozen or so posts that are only a thank you for pointing this out are removed to prevent excessive clutter! So there is no need to thank me, I'm just happy to bring this to peoples' attention! But if you just gotta, a PM is fine :)

Don't lose access! Your local public library probably provides access to JSTOR, and library cards are free. You will lose access to many databases (e.g. ScienceDirect), but JSTOR, Proquest Historical Newspapers, and Academic Search Complete are commonly offered by public libraries. If your local library does not offer these, you can typically get a library card for any system in your state, and chances are the major metropolitan systems do offer access.

I threw together a hodgepodge list of interesting (to me) articles on Mesoamerica a while back for someone who pm'd me a similar request. Aside from all the other advice about keeping access, JSTOR offers free limited accounts. You can "check-out" 3 items at once, each of which stays on your "bookshelf" for 14 days minimum. It's so convenient that I use it when I'm outside the Ivory Firewall and don't feel like using my remote access.

Anyway, here's that list (I picked out a few in italics which are more recommended):

Agriculture & Diet

Santley & Rose 1979 Diet, Nutrition and Population Dynamics in the Basin of Mexico

Evans 1990 The Productivity of Maguey Terrace Agriculture in Central Mexico during the Aztec Period

Pohl et al. 1996 Early Agriculture in the Maya Lowlands

Taube 1996 The Olmec Maize God: The Face of Corn in Formative Mesoamerica

Merrill et al. 2009 The Diffusion of Maize to the Southwestern United States and Its Impact

Piperno 2011 The Origins of Plant Cultivation and Domestication in the New World Tropics Patterns, Process, and New Developments

Minnis & Whalen 2010 THE FIRST PREHISPANIC CHILE "(CAPSICUM)" FROM THE U.S. SOUTHWEST/NORTHWEST MEXICO AND ITS CHANGING USE

Crafts & Trade

Drennan 1984 Long-Distance Movement of Goods in the Mesoamerican Formative and Classic

Rafferty 1990 The Virgin Anasazi and the Pan-Southwestern Trade System, A.D. 900–1150

Charlton et al. 1991 Aztec Craft Production and Specialization: Archaeological Evidence from the City-State of Otumba, Mexico

Hosler 1995 Sound, Color and Meaning in the Metallurgy of Ancient West Mexico

Hosler & Macfarlane 1996 Copper Sources, Metal Production, and Metals Trade in Late Postclassic Mesoamerica

Dewan & Hosler 2008 Ancient Maritime Trade on Balsa Rafts: An Engineering Analysis

Politics & War

Barlow 1945 Some Remarks on the Term "Aztec Empire"

Rounds 1979 Lineage, Class, and Power in the Aztec State

Isaac 1983 Aztec Warfare: Goals and Battlefield Comportment

Isaac 1983 The Aztec “Flowery War”: A Geopolitical Explanation

Kurtz 1984 Strategies of Legitimation and the Aztec State

Brumfiel 1985 Aztec State Making: Ecology, Structure, and the Origin of the State

Smith 1986 The Role of Social Stratification in the Aztec Empire: A View from the Provinces

Smith 1987 The Expansion of the Aztec Empire: A Case Study in the Correlation of Diachronic Archaeological and Ethnohistorical Data

Smith 1987 Archaeology and the Aztec Economy: The Social Scientific Use of Archaeological Data

Carrasco 1995 Give Me Some Skin: The Charisma of the Aztec Warrior

Lucero 2003 The Politics of Ritual: The Emergence of Classic Maya Rulers

Spencer & Redmond 2004 Primary State Formation in Mesoamerica

Other

Coe 1962 Costa Rican Archaeology and Mesoamerica

Moser 1973 Human decapitation in ancient Mesoamerica

Fox et al. 1981 The Late Postclassic Eastern Frontier of Mesoamerica: Cultural Innovation Along the Periphery

Smith 1984 The Aztlan Migrations of the Nahuatl Chronicles: Myth or History?

Ortiz De Montellano 1985 Counting Skulls: Comment on the Aztec Cannibalism Theory of Harner-Harris

Kellogg 1986 Aztec Inheritance in Sixteenth-Century Mexico City: Colonial Patterns, Prehispanic Influences

Justeson 1986 The Origin of Writing Systems: Preclassic Mesoamerica

Read 1987 Negotiating the Familiar and the Strange in Aztec Ethics

Fox et al. 1996 Playing with Power: Ballcourts and Political Ritual in Southern Mesoamerica

Haslip-Viera et al. 1997 Robbing Native American Cultures: Van Sertima's Afrocentricity and the Olmecs

Joyce 1998 Performing the body in pre-Hispanic Central America

Pohl 1998 Themes of Drunkenness, Violence, and Factionalism in Tlaxcalan Altar Paintings

Carrasco 1999 Uttered from the Heart: Guilty Rhetoric among the Aztecs

Hicks 1999 The Middle Class in Ancient Central Mexico

Elferink 2000 Aphrodisiac Use in Pre-Columbian Aztec and Inca Cultures

Joyce 2000 Girling the Girl and Boying the Boy: The Production of Adulthood in Ancient Mesoamerica

White et al. 2000 Testing the Nature of Teotihuacán Imperialism at Kaminaljuyú Using Phosphate Oxygen-Isotope Ratios

Barker et al. 2002 Mesoamerican Origin for an Obsidian Scraper from the Precolumbian Southeastern United States

Joyce et al. 2004 Lord 8 Deer "Jaguar Claw" and the Land of the Sky: The Archaeology and History of Tututepec

Duncan et al. 2008 Human Cremation in Mexico 3,000 Years Ago

Price et al. 2008 Strontium Isotopes and the Study of Human Mobility in Ancient Mesoamerica

Vargas et al. 2009 Daily Life of the Ancient Maya Recorded on Murals at Calakmul, Mexico

Keith Hopkins' "Novel Evidence for Roman Slavery" is one of my all time favorite papers. It is really brilliant both in what it says and in how it lays out its methodology, and it is quite readable.

What are your interests? If it is critical theory or related to Japan I have some suggestions.

EDIT:

I want to preface by saying that anyone interested in Japan and not yet privy should definitely check out The Asia-Pacific Journal it is a free journal that puts out really great stuff every week. While mainly focused on Japan, there are often articles on other places in the region. While not peer-reviewed many of the articles published are from scholars who do publish in Monumenta Nipponica, Harvard Journal of Asiatic Studies, etc. That is to say, they are academics, know the game and the articles published are valuable.

With that said, here are the ones behind 'the ivory firewall' (saw that somewhere in this thread and liked it)

Pre-Modern

• Rescuing the Nation from History: The State of the State in Early Modern Japan Land and Lordship in Early Modern Japan by Mark Ravina; Mercantilism in a Japanese Domain: The Merchant Origins of Economic Nationalism in 18th-Century Tosa by Luke S. Roberts Review by: Ronald P. Toby Monumenta Nipponica, Vol. 56, No. 2 (Summer, 2001), pp. 197-237 Published by: Sophia University Stable URL: http://www.jstor.org/stable/2668408

Post-War

• Triumphal and Tragic Narratives of the War in Asia John W. Dower The Journal of American History Vol. 82, No. 3 (Dec., 1995), pp. 1124-1135 Stable URL: http://www.jstor.org/stable/2945119

• Exporting Democracy?: American Women, "Feminist Reforms," and Politics of Imperialism in the U.S. Occupation of Japan, 1945-1952 Mire Koikari Frontiers: A Journal of Women Studies Vol. 23, No. 1 (2002), pp. 23-45 Stable URL: http://www.jstor.org/stable/3347272

Ryukyu/Okinawa

• Ambiguous Boundaries: Redefining Royal Authority in the Kingdom of Ryukyu Gregory Smits Harvard Journal of Asiatic Studies Vol. 60, No. 1 (Jun., 2000), pp. 89-123 Stable URL: http://www.jstor.org/stable/2652701

• Between War and Tropics: Heritage Tourism in Postwar Okinawa GERALD FIGAL The Public Historian Vol. 30, No. 2 (Spring 2008) (pp. 83-107) Stable URL: http://www.jstor.org/stable/10.1525/tph.2008.30.2.83

• Taku Suzuki (2006) BECOMING “JAPANESE” IN BOLIVIA: OKINAWAN- BOLIVIAN TRANS(NATIONAL)FORMATIONS IN COLONIA OKINAWA , Identities: Global Studies in Culture and Power, 13:3, 455-481 http://www.tandfonline.com/doi/abs/10.1080/10702890600839652 (Not JSTOR, but your library probably still has access and very interesting)

Literature

• Fractious Memories in Medoruma Shun’s Tales of War Davinder Bhowmik, The Asia-Pacific Journal, Vol 10 Issue 38, No. 3, September 17, 2012.http://www.japanfocus.org/-Davinder-Bhowmik/3830/article.html (Free)

• Five Stories by Kunikida Doppo Author(s): Kunikida Doppo and Jay Rubin Source: Monumenta Nipponica, Vol. 27, No. 3 (Autumn, 1972), pp. 273-341 Published by: Sophia University Stable URL: http://www.jstor.org/stable/2383917

• Murakami Haruki and the cultural materialism of multiple personality disorder John Whitter Treat. Japan Forum, 2013 Vol. 25, No. 1, 87–111, http://dx.doi.org/10.1080/09555803.2012.741142 (again, not JSTOR)

You can also hang out in /r/Scholar, where people who wish they had Jstor access ask stuff to people who do.

I suggest

• A Dual-Processual Theory for the Evolution of Mesoamerican Civilization by Richard E. Blanton, Gary M. Fienman, Stephen A. Kowalewski, Peter N. Peregrine

• Social Identity and Ethnic Interaction in the Western Pueblos of the American Southwest by Tammy Stone

• Toward an Ethnology of Mesoamerican Customary Social Units by Eileen M. Mulhare

• Architecture and Energy: An Evolutionary Perspective by Elliot Abrams

• Architectural Energetics, Ancient Monuments, and Operations Management by Elliot Abrams and Thomas Bolland

• Recent Research in West Mexican Archaeology by Helen Pollard

• Recent Research in Western Mexican Archaeology by Christopher Beekman

• Corporate Power Strategies in the Late Formative to Early Classic Tequila Valleys of Central Jalisco by Christopher Beekman

• Controlling for Doubt and Uncertainty through Multiple Lines of Evidence: A New Look at the Mesoamerican Nahua Migrations by Christopher Beekman and Alexander Christensen

• A Decipherment of Epi-Olmec Hieroglyphic Writing by John Justeson and Terrence Kaufman

• Recent Developments in Cypriot Prehistoric Archaeology by Stuart Swiny

• Prehistoric Cyprus: A Current Perspective by Stuart Swiny

• Of Cows, Copper, Corners, and Cult: The Emergence of the Cypriot Bronze Age by Stuart Swiny

JSTOR has free accounts for individuals that allow you to read three articles every fortnight/78 annually.

I believe JSTOR offers discounted access to independent scholars who are members of the AHA or OAH.

What topics are you interested in?

I found When is food a luxury by M van der Veen to be an interesting paper. Not sure how well it holds up in comparison to other papers on the topic, but it's interesting and the subject matter is relevant outside of pure academia.

The Many Headed Hydra by Rediker (William and Mary Quarterly, I believe)! Excellent and foundational article that later became a book. It makes the case that sailors throughout the Atlantic World were behind much of the unrest and revolutions in the 18th c.

I compiled a list of my interests, then used search terms to browse recent papers. Do you like nootropics? Use those terms. Interested in sexuality? Adoption? Volcanoes? There are so many options/topics.

These aren't strictly JSTOR, but you might have access anyway, and these are great articles.

• Pregnancy, Childbirth and the Female Body in Early Modern Germany by Ulinka Rublack is a fascinating read I really enjoyed. [edited in JSTOR link]
• Beyond Discourse Theory by Lyndal Roper was my go-to cite-this-to-sound-clever article, but it's genuinely a brilliant article on the limitations of discourse theory and the need to analyse emotional experience as part of cultural history, and uses a 17th century Swiss man's experience of "demonic possession" as a case study, which is always fun to read.

I don't have my old reading lists here right now, but I'll update this once I have access again.

You know about Library Genesis and Sci-Hub, right? Just paste a DOI or Title or even link there — and get a full-text instantly.

These largest in the world underground free archives of nonfiction scans and access proxies are the only Russian things I'm proud of as a Russian.

All of them!

Seriously though, I would say pick the ones that fit what you want to continue pursuing the best.

There are some general historical articles, but I really, really wish I would have had some copies of articles I read in grad school now, especially some of the ones I used in my thesis, but did not print off.

Some universities will have Alumni Access, others won't. I ended up teaching back at the university I graduated from, so I have access again.

I think the body of works present in online databanks, including JSTOR, is so vast that I'd rather advise you to find a way to keep access to these databanks than to download a few articles. Also, I've always used it as a tool to get articles and never really remembered which ones I got on that specific database.

My favourite JSTOR article is "The Liberal Order Framework" by Canadian Historian Ian McKay. It's a fantastic analysis of trends in Canadian history and his thesis that Canadian history ought to be looked at as a centralized project of national rule really reverberated with me.

I interpret this question as op wanting more of a "what's your favorite history journal article" rather than "how to get access", oh well. I recommend Cities and States in Europe, 1000-1800 by Charles Tilly, but If you're interested in for example Marriage, family and household history, a lot of the "classic" articles by Hajnal, Berkner and Laslett are up there, the theories are still very interesting though more problematic today with all the new source material that has been uncovered in the last 20 years.

If you are Victorian, you can access JSTOR at anytime for free through the State Library of Victoria provided you sign up to be a free member beforehand.

If you are interested in social cooperation and how groups, organisations and civilisations can thrive without a central governing agency (a state), I recommend you download everything you can by Peter T. Leeson.

Sure, he is an economist. But most of the economic theories have historic context.

Some of the best are: An-arrrr-chy: economics of Pirates Human Sacrifice Law of the Lawless Gypsy law Better of Stateless

and so on and so on... he is by far a personal favorite at the moment.