Avoid Tinypic unless you only need to post one picture at a time (without any albums or galleries). Tinypic is wonderful for enabling people to post a link (on this site for example) to an individual picture but useless for general image hosting (which it's not designed for).
Some photo storage sites only host 'private' galleries. i.e. they can only be viewed by people who've you've provided with a link and/or password. That's fine if you only want to show your pictures to friends and family members but useless if you want to share your pictures with a wider audience. The better sites (in my opinion) are those which permit you to choose whether individual galleries are 'public' or 'password protected'.
The biggest site in the world is definitely one of the best. It's the (US-based) Webshots:
http://www.webshots.com/
Photofile (which is Russian-based) is also good:
http://photofile.name/index.php#
(If that link displays in Russian, click on the Union flag)
The real star performer though, is the little-known service provided by a French guy called Alex Madon. He runs the superb Atpic website, which offers unlimited free picture and video hosting (with loads of features available) totally free of all advertising material:
http://atpic.com/
Chris