Well, you could e-mail game website owners to publish your game there, if it's a full-fledged, complete, enjoyable flash game, enough to call it professional. But if you want to just upload .swf files generally, search 'SWF hosting site' or something like that. Sites include
http://www.swfcabin.com/ and some sites like
http://www.imageshack.us/ let you upload .swf files as well.
If you're looking for a site like Newgrounds, then I've got nothing. There's the
http://www.stickpage.com/ portal (look at the link at the top of the homepage for a link), but stickmen are pretty much a must-have theme over there, and the site is down for who knows how long for updates.
_________________Previously buzzer465 - I just remembered this account existed after like 4 years...
Tall hat Kirby! Edited off the SSF2 Kirby.