LaLa.com allows you to upload your collection of mp3's and then stream them from anywhere, for free.
If you use their software to upload your music, for the more mainstream stuff they have license to sell, it's rather quick, because they match your collection against what they carry, and if they have it, they just add it to your account immediately. Anything they don't have, they make you actually upload. (make sure your collection is properly tagged!)
They do have individual file size limits, both minimum & maximum. They do not have any limits to the total amount you can have in your account, though.
It's kind of "one way" though. You can upload it, but you can not download it again later. So this isn't for file backup purposes.
It's good for streaming your collection when you are away from home, without taking the collection with you. Their online player for streaming is quite nice. You just log in and keep it open on a tab of your browser and you can listen all day, every day.
It's also a last.fm style social network, where you can follow other people (I don't). And supports scrobbling what you play to last.fm.
For music you do not own already, you can purchase "perpetual" streaming rights for around $0.10 per song. And if you decide later to buy the mp3, they will credit you the $0.10 you already paid, off the price of the mp3. They even start you out with 50 free songs when you sign up (streaming only) and the first stream of any song they have is free, so you can preview it and decide if it's worth paying to hear it again.