photobucket is great. as nutmeg has said it is free and only takes a few minutes to sign up.
downside is the ad but as its free you can just ignore them, and the fact you only have 1gb of storage space. but as the free accounts limit you to sizes, iirc, 800x600 then its an offy lot of photos to fill up.
pro account is better if your saving alot of photos - and i mean alot, unlimited storage and FTP uploads means no sitting waiting about on the webpage for them to load.
You can use www.tinypic.com or www.imageshack.us to upload photos without an account, but they aren't saved anywhere and I think they are deleted after a few months. Photobucket photos won't be deleted so it's probably best to use that so your photos are safe.
Photobucket is loads easier in all aspects I think, getting the URL code, editing etc... the only thing I prefer about Flickr is you can post an image at a certain size without having to resize your photo completely.