http://evernote.com is a great place because you can choose the option of not downloading the software, but just using your web browser instead. The free account only gives you 40MB of space, but if you are just using text notes you should have room for plenty (about 20,000). It has the option not to download, and is free (unless you need more space, in which case you can get Evernote Premium for $5, but you should have plenty of room). You can also add web clips, camera phone photos, audio, and high resolution photos. But if you just need text-only notes, then you should have plenty of room every month for notes.
