I have used Photobucket for years, mostly to host non-photography related images... stuff for boards and such.
When I got into Photography I discovered their system trashes images. The system compresses them, or otherwise modifies them so that pictures often look slightly off. Not horrible, but noticeable to me in many cases. The nice thing about Photobucket is that it's free up to a point. I paid $20 a year to have an unlimited account and I keep all of my junk images there. They also have a deal with Target so friends and family can print images and pick them up locally. Handy, but the print quality is marginal at best.
So I began a quest to find a photography oriented website. That, and I created my own site too (
http://www.intempus.us).
The site I found with the best image quality and which allows you to control that image quality (you can set default sharpening, etc. or turn all modifications off) is
SmugMug Photo Sharing. Your photos look better here..
Smugmug has three different subscription plans. One for personal use, one for heavy use and another for professional use. I really like this system because unlike Photobucket, Flickr, ImageShack, etc. you can fully customize your page and even point a custom URL to your directory (they are partnered with GoDaddy). Here's an example of my SmugMug system I just set-up:
inTempus Photography- powered by SmugMug
SmugMug also has great printing services. They mail you the prints, but they look amazing. I think they have one of the best printers out there, or so far that I've found. Friends and family can order prints from your page. The site also works with the iPhone (special free app). You can geotag your images and have them appear on your home page. It's a very cool feature.
If you sign up for SmugMug, use this code
KAMvZpioBsAvk and you'll save $5.
I hate Facebook, it completely trashes images. Black and White images are completely washed out as are the colors in color photos. Forget that option. MySpace is a joke too...
I haven't tried Picasa yet. I probably won't given my recent discovery of SmugMug.
Flickr pains me because I hate their menuing system. I think it's horribly laid out. But some folks like it. I have an account, but given the lack of customization I avoid the system.
YMMV