I know that some of our best historians have a very large variety of sources to base their research on, but what about young graduate students or professors? I am about to start my Ph.D. in sociology and am interested in doing comparative historical research. Are there any major databases that every young/budding historian knows about?
Your university library is very likely to have a history specialist or "liaison librarian" for history. Ask at the front desk who that person is and make an appointment with them to get acquainted with the major resources in your area.
It sounds like your asking about statistical data, such databases as Nationmaster.com can be useful. But journals often have articles with statistical data from surveys going way back. As do books. If you use google to find a book or journal, and reference the source of the stats/data as well as the book/journal it's in, this makes the reference section of the work look very well researched.
I often refer to http://www.eigenfactor.org for finding the best/most renoun journals.
Books. Universities have a faculty library and some (Oxbridge) have college libraries from which you can borrow books. Also, Jstor is a must to read articles and reviews. Tutors also have their own personal libraries and they might lend to students, but that depends on the character of the tutor.
Are you talking DATA data or just papers?
Databib.org has a couple of history-focused data repositories listed, data.gov is a good starting point for governmental data for American history. It depends on what sort of data you need!
Lately I've been making my own dataset for castrati, because there aren't any open datasets for my research really (if there are any at all, which I doubt).
What time period?