Most of these databases cover open access theses and dissertations, which you can download at no charge. If the one you want isn't available, request through Interlibrary Loan.
Along with the resources listed below, you can also search dissertation collections for Canada, Australia, Austria, Germany, Portugal, Brazil, The Netherlands, South Africa, and Scandinavia.
Google and Google Scholar are also good places to search for open access theses and dissertations.
ProQuest's Dissertations & Theses (PQDT) is the best starting point for finding dissertations, indexing more than 3.8 million dissertations and theses from 1743 to present, though with greater coverage of dissertations.