Luckily, I have a bookmark folder set up with links to the sites I frequent for TS3 downloads. I pretty much visit each site once a day.
Mod The SimsAlways my first stop. The most quality TS3 cc of any site. But everyone knows about MTS since it was around in the TS2 days, so I won't say much more about it.
TSROccasionally I'll find some decent stuff here. Unfortunately, most of the high quality stuff is subscriber only. Most of the clothes I got from here have meshes that cause strange lighting, like there's dark black shadows where there should be light and light where it should be shadowed, or clothes that have incorrect bump maps or other problems with the textures. Now I'm wary about downloading any clothes from there. Since everything on the site is in Sims3Pack format, you have to uninstall through the launcher which doesn't always delete the items. Like I downloaded a hairstyle I didn't like, and even though it's gone from the launcher, it's still in my game, even after deleting the cache files.
Liana Sims 3She doesn't update too often, but there are some nice clothes here. I especially like her jeans. They look much more realistic than the ones that come with the game.
All About StyleThis was my favorite Sims 2 site, and it's now my favorite Sims 3 clothing site. Everything looks great in game and all the textures are high quality.
Simcredible DesignsThey don't have a lot yet, but there is some nice modern furniture sets there as well as some patterns.
Peggy ZoneAnother well-known site from the TS2 days. Lots of hairstyles and some clothes there. Just be sure if you download from the site not to use the resource.cfg file she includes. Actually, ignore her installation instructions and just use Delphy's Install Monkey program.
Rose SimsNice hair, but most of it is donation only. Her hair tends to look much darker than other meshes for some reason. I had a sim with light blonde hair, and when I picked any of Rose's hairstyles, the hair looked dark brown without me changing the hair texture. It's not an issue for sims with dark hair, though. There's some nice clothes, but if you use Delphy's breast sliders from MTS, they will look deformed.
Stylist SimsLots of nice modern furniture here and some nice clothes.
SimPossibleAnother site without a lot of content yet, but they have these great paintings. There's beach paintings as well as fashion and modern art themed paintings and they look great in the game. I use them in every single house in my game.
Savio's StuffThe majority of the hairstyles I use in my game come from here. He takes popular Sims 2 hairstyles and converts them to TS3. They're all nicely done, too, with working recoloring sections (roots, tips, etc) and no noticeable gaps or transparency issues.
XM SimsThey have some cute hairstyles that look good in game. *WARNING: Be careful going there if you don't have AdBlock Plus or similar and anti-virus software. Several people have reported some of the ads there have trojans. I have AdBlock Plus and an anti-virus program, so I haven't had any issues, but I wanted to warn anyone about the site just in case.
SailfinSims *Registration required*
This is a forum I found originally because someone linked to the two gorgeous hairstyles Nouk posted there. There are other nice downloads as well, but the Nouk hairstyles (including a really wavy/curly hair) alone are reason enough to register.
Vita Sims 3I didn't find this site until recently, but they have some nice object sets. There's a nice ultra modern-looking living room set and a super cute nursery, so it's worth checking out.
Sims 3 BlogSo this site doesn't actually have downloads, but I frequent it because it points out where the Sims 3 updates are, so I don't miss any good downloads. It's where I found most of the hairstyles in my game.
Lili SimsI just found this site. They have some nice clothes, but what I really love is the boots. There are high heeled boots in pretty much any height you could want from ankle height to ones that go up to the thighs. The textures on them look great and they're fully recolorable.
That's it for now. I'll add more if I find any worth mentioning.