I (sort of) echo SharpByCoop's advice. I have no experiece with Fototime.com, which he suggests – however I agree with his recommendation of a pay site, and his comment that free sites have drawbacks.
Simply put, paid sites stay accountable to their customers, while free sites don't necessarily have to. They also tend to stay around for the long-term, more consistently, since they have a business model that actually brings in income. So, they're less likely to be a fly-by-night operation, with your hosted pictures suddenly disappearing, one day. If you want a site that will let you post as much as you want, that won't overly compress your pictures, that won't censor your pictures, that maintains good internet hygiene and won't give you viruses, trojans, worms, and various malware – if you want a quality hosting site, then pay for it.
I have my own website, which I pay for, and I also have a few flickr.com accounts, which I pay for. Flickr is a great option, for unlimited number of pictures of any file size for $25 per year; they can also be used for free, for up to the first 200 pictures.
Flickr has the benefit of being one of the largest such sites around, giving them stability, and giving them a stake in maintaining quality. On the higher end, Zenfolio offers great hosting of unlimited full size files, along with fullfillment options and other features, for $100 per year.
If you're only considering free options, then facebook is probably a good choice. While they limit the size of your pictures, they are stable, they correct problems, and they'l host an unlimited number of pictures.
Also, read this thread:
http://www.bladeforums.com/forums/showthread.php?t=382831&highlight=free+photo
(By the way, the person in the other thread who recommends photobucket right before my post [Rat F.] has, since then, lost almost all of his photobucket-hosted pictures, as I recall.)
And check out this thread:
http://www.bladeforums.com/forums/showthread.php?t=707342&highlight=virus