I use Flickr quite a bit. They have a limit on how many pictures you
can post in a month but you are allowed quite a few.
The limit is on how much data you upload, not how many photos. If you
reduce the size of your files (use something like Faststone Photo
Resizer), you can upload more.
The limit on paid-for accounts is much higher and I think would be
adequate for almost all needs.
I've had some
images posted there for over a year and they haven't been deleted yet.
And they won't be. If you have a free account, there is a limit of
200 photos in your Photostream (i.e. that you can scroll through),
and as you upload more photos, the oldest photos will disappear from
that, but they are still there, can still be accessed if you have the
link to the photo's page, can still be used in blogs etc (the link is
still valid), and are still stored on Flickr's servers. If you
upgrade to a paid-for account, all the photos you uploaded will once
again be available in your Photostream.
Flickr is especially good for photographs because there is an option
for making a Flash presentation of your photos.
There are quite a lot of options, and even more at
www.flagrantdisregard.com. There are also third-party add-ons, such
as plugins for WordPress etc which make it easier for you to use your
photos in a variety of ways.
I would second the recommendation for Flickr - a free account does
quite a lot.