I'll throw in a plug for
photobucket as it seems the easiest to use for me. No apps to download and install (so I can access my account from any computer, including at work); and it doesn't require others to create an account just to look at your photos. Also easy for others to get a copy of the entire album in one ZIP file (which appears to be impossible from Picasa & Flickr).
And it's easy to get the IMG links that are needed to make your photos appear on BCF, too. When you hover your mouse over a photo in album view, a pulldown appears with the various kinds of links to that photo. Click on the "IMG Code" box,
press Ctl-C (assuming you use Windoze), then switch to your BCF post and press Ctl-V. While you are composing your post, it will look something like
<div class="ubbcode-block"><div class="ubbcode-header">Code:</div><div class="ubbcode-body ubbcode-pre" ><pre>
</pre>[/QUOTE]
but when others view the post (or you use "Preview"), it will appear as