I often see people asking for data, databases, and similar resources, so I thought it would be nice to start a dialogue in which we can share one's we know of and learn of those others use. Naturally, it's only fair that I go first. Below are just those I have in my favorites/bookmarks folder for IE/Chrome, minus all the databases for papyri and other extant manuscripts as well as those containing collections of texts written in ancient Greek, Latin, Sanskrit, Syriac, etc.
Face Databases
http://vision.ucsd.edu/content/yale-face-database
http://vision.ucsd.edu/content/extended-yale-face-database-b-b
Links to face databases
http://www.face-rec.org/databases/
http://web.mit.edu/emeyers/www/face_databases.html
Multifunction Databases/datasets
http://ftp.ics.uci.edu/pub/machine-learning-databases/
http://lib.stat.cmu.edu/datasets/ (StatLib Datasets Archive)
http://www.statsci.org/datasets.html (StatSci Data sets)
http://physionet.org/physiobank/database/ (PhysioBank currently contains over 40,000 recordings of annotated, digitized physiologic signals and time series, organized in over 60 databases (collections of recordings). All are freely available from PhysioNet)
http://biostat.mc.vanderbilt.edu/wiki/Main/DataSets
Corpora for linguistics & NLP
http://corpus.byu.edu/ (home of COCA, BYU's BNC, GlobWbe, Wikipedia Corpus, etc.)
http://verbs.colorado.edu/verb-index/ (Unified Verb Index: links to VerbNet, PropBank, FrameNet, & OntoNotes)
http://wordnetweb.princeton.edu/perl/webwn (WordNet Online; downloadable from the home page links)
http://multiwordnet.fbk.eu/english/home.php (MultiWordNet)
Microarray databases:
http://smd.princeton.edu/
http://www.broadinstitute.org/scientific-community/data
http://www.tech.plym.ac.uk/spmc/links/bioinformatics/bioinformatics_data.html Bioinformatics Data links to datasets (some are down)
Important Statistics Organizations with publications and datasets
http://ec.europa.eu/eurostat
http://www.bjs.gov/index.cfm?ty=dca (Bureau of Justice Statistics)
http://www.icpsr.umich.edu/icpsrweb/ICPSR/index.jsp (Inter-university Consortium forPolitical and Social Research)