Tests and instruments are commonly referred to as published or unpublished. Published means just that and that the item is likely under copyright. In order to gain access to such a test or instrument, you must contact the publisher. Unpublished tests or measures are often, but not always, shared in the literature that mentions them. PsycINFO, the database, does include a useful feature to locate articles that use certain tests.
Youtube video on how to choose and locate an instrument.
First off, try PsycTests from the American Psychological Association. Then, try these other sources:
Test Link--from the Educational Testing Service. Contains a searchable database of over 25,000 tests. Some tests avaialble from the early 1900's, but focusing on 1990s- present. Test material is mostly from American publishers with some tests from the U.K. and Canada.
Health Sciences and Research Resources Database-- Sponsored by the National Library of Medicine. Focuses on data sets, instruments, survey, etc in the health and behavioral sciences. Does not contain full-text of instruments, but does include contact information for obtaining them.
Psychological Tests for Student Use--Offered by York University, this webpage gives access to a small, but useful set of test instruments for student use. *The copyright holders have generously waived the requirements to seek their permission.
National Quality Measures Clearinghouse--NQMC is an initiative of the U.S. Department of Health and Human Services. This website contains a database for information on specific evidence-based health care quality measures and measure sets.