For many years, UMI/Proquest has microfilmed U.S. and Canadian dissertations and sold microfilm and print copies to libraries and scholars. Since 1997, they have also made digital versions available online to institutions that subscribe to Proquest Dissertations & Theses (which used to be called Dissertation Abstracts International). The DAI database extends back to 1861 and represents the work of authors from over 1,000 North American graduate schools and European universities. Some 60,000 new dissertations and 12,000 new theses are added to the database each year. Those published from 1980 forward also include 350-word abstracts, written by the author. Citations for master's theses from 1988 forward include 150-word abstracts.
Older dissertations are available for a handful of schools (those which have made arrangements with ProQuest to digitize their older dissertations.) New ones are added steadily, so it's worth checking.
DAI can be searched by topic, by school & department, or by adviser (starting with 1989). Use the Advanced Search interface, and be inventive. The subject indexing is extremely general, and the keywords are drawn from the title and abstract, or are those provided by the author, so they can be very inconsistent. To see which schools are included for a particular country, use the Advanced Search, School Index, and search by the name of the country, e.g. "france."
If you request a US dissertation through Interlibrary Loan, generally they will purchase it from UMI for the library. (Dissertations that are not held by UMI, e.g. Harvard dissertations, are more difficult to obtain.) Canadian dissertations can be obtained through ILL from the National Library of Canada on microfiche. Canadian theses are indexed in Theses Canada from 1965, with full text from 1998.
ProQuest Dissertations & Theses - UK & Ireland (1716+) Bibliographic listing of dissertations and theses, most with abstracts, accepted for higher degrees by universities in the United Kingdom & Ireland.