Perhaps not the most 'couth' place to listen to classical music, but lately I've been doing quite a bit of it - partly through laziness and partly because it's a lot cheaper than constantly buying new CDs!
There is really a lot of range, with some wonderful performances on there. You sort of have to know what you're looking for, but if you aren't quite sure, then I would recommend exploring some of these channels:
This seems to be the most popular channel, with over 30 million upload views. 138 uploads to choose from, mostly big hits. This is the place to go to if you just want to browse some great classics. Here is one example.
The Garden of Harmony
Fantastic channel, with 728 uploads to choose from. Loads of Vivaldi and Bach, but not only Baroque. This recording of Beethoven 5: II is perhaps the best I've ever heard.
Lovely channel. I've enjoyed every piece I've listened to on here. Wide range of composers without specialising in any one thing, though I suppose it's mostly the Romantics. This is a wonderful bit of Wagner.
Lots of good stuff on here (149 uploads). I have found that the quality of recordings are in general not as good as the other three, but it's well worth a browse. Example.