UPDATE: Great additional list from Or Shai in the comments:

http://www.tradersnarrative.com/list-of-proprietary-trading-firms-735.html

This could be useful for finding a job or just Googling out of curiousity. This is a secretive industry so it can be hard to tell which firms are important.

From Nuclear Phynance:

Banks -
Goldman Sachs
Morgan Stanley (PDT or ETL)
Barclays
Deutsche
JP Morgan

Hedge Funds -

Athena Capital Research

D.E. Shaw
Two Sigma
Millennium / World Quant (masters level+)
Renaissance
HBK (not hiring)
Citadel (no positions listed, accepting resumes)
IV Capital (only career email listed)
Tower Research (only back office internships)
Knight (only 2 back office jobs listed, not internships)
Blue Crest (minimum PhD for front office)
Winton Capital (UK based, winter internships)
GSA Capital (only career email listed)
Etc.

Prop -

Hudson River Trading (only C++)

Wolverine Trading (Internships)

Optiver (No internships)
CTC (Chicago Trading Company) (Trading assistant TA)
Fox River Partners (No website)
Jump Trading (Internships)
Spot Trading (Career website down)
GETCO (No internships)
Sun Trading (No internships)
Matlock Capital (Tiny, no positions)
Ronin Capital
Allston Trading (Software developer internsips)
Chopper Trading (No internships)
Tradelink (No internships)
Etc.

It would be great to extend this list, please leave a comment with additions.