I teach an undergraduate general history course which provides a kind of broad strokes view of major historical developments e.g. the Ancient World, the Middle Ages, etc.
I have had great success with one of my earlier sessions where I brought two historical artefacts to class to show students. The first was part of my collection of Roman Coins. I have a few worse for wear coins which I actually allowed the students to touch, while a few higher quality coins were used to display the text on the coins, which of course uses the same alphabet as we (in western countries) use today. The students greatly enjoyed this. Another 'artefact' was an ancient Greek song from YouTube. I find the use of these objects help make students enthusiastic about the field of history, and possibly consider becoming historians themselves.
I would like some suggestions of ways of bringing authentic historical objects into classroom. This can include online resources (like the song) but ideally also cheap physical objects from different civilizations and periods.
Since my speciality is Early Modern Europe I intend to bring perhaps a print or archival type document or book from the period. I can also use high resolution images of paintings available online, but something to touch would be nice too. The modern period should also be easy to find stuff on. But I am at a loss what objects I can collect from other periods and places.
My first recommendation is always coins. Being able to contrast contemporary coins--say, medieval Christian and Islamic--usually goes over pretty well.
Another option, maybe a bit pricier, is replica weapons. The greatest success I have EVER had is with a replica (accurate to 12th century) sword I had borrowed. Check with your local Renfair and Society for Creative Anachronism group. Those are the people with the accurate replicas. On that note, I once brought in someone from our SCA chapter to show off a couple of their period-accurate costumes, too, which was a big hit.
Cooking period-accurate food for the class, of course, is the best way to win undergraduate hearts.
ETA: I'm going to drop a link to this thread in Theory Thursday, a thread that attracts discussion about history in academia, so it gets more visibility.
An interesting and accessible type of document is a high quality print of important artefacts. for example a color reproduction of a page from the Gutenberg bible, DaVinci's schematics, etc. As for objects, i often use elements that are non-historical in order to illustrate historical themes. For example, i can bring an element of iron and an element of copper (then titanium aluminum for more modern times) into class for students to manipulate and compare.
Another artefact that can interest are medals. In any cases, i have to agree with \sunagainstgold that weapons (or weapon reproductions) always elicit a great deal of fascination from any students.
If you have a pocket-watch (I know this would be expensive) from the industrial revolution or roughly that time, you could connect it to EP Thompson's "Time, Work-Discipline, and Industrial Capitalism."
I've got mixed feelings on this. Of course there's something special about having some sort of tactile connection with the past. But more often I think the cost is too great. Historical objects can be damaged or lost. Or perhaps worse yet, buying historical objects can encourage all sorts of unethical behavior—clipping illuminations out of manuscripts, selling an early Bible sheet by sheet, encouraging treasure hunters to outpace the archaeologists. And the benefits for most undergrad courses are too few. Unless the students already have a strong sense of historical significance, the authenticity of these artifacts won't mean a whit.
I'd say your two best bets are museum shops and reenactors. Museum shops tend to have a great selection of objects that are considered historically significant by the people who curate the museum and by the self-selecting segment of the population that visits museums. Usually these are the things that can fall neatly into lectures based off a textbook.
Reenactors, in contrast, are the self-selecting segment of the population that gets excited about historical objects without necessarily understanding their historical significance (although the best of them could certainly be experts in their field). The things that they curate and replicate are the things that get people excited about history, and usually they're not the bulkiest or most expensive items possible. It's a blast to talk to them and figure out what their priorities and interests are, and often to see just how far they stray from my own interests in the period. The reenactors I've met are almost all uniformly generous with their time and knowledge. A few conversations can be enough to write a lecture, and if you find the right ones, you might even be able to recruit a guest lecturer.
Reenactors get very excited about glass beads, for example, so I carry a handful with me wherever I go. The beads tend to spark similar excitement among people unfamiliar with the middle ages, and for those who are already excited about medieval things, it gives me the opportunity to open up conversations that will hopefully get them to appreciate new dimensions of their significance.
I've been trying to put together a handlist of websites selling early medieval replicas. Check it out!