Self-hosted solutions:
If you have a domain or a subdomain and sufficient amount of web space to go with it, you can use a gallery solution.
Dynamically generated galleries that include an administration interface for uploading photos and managing your online galleries can be quite nice, you can find a short list here:
http://opensourcecms.com/ (click on Image Galleries in the menu on the left).
I can recommend Coppermine and Gallery 2.
If you need more than a gallery, something like
a personal website with a contact form and a gallery, I suggest using
Jaws or
Dragonfly CMS (Dragonfly integrates Coppermine gallery). There are more, but I found these two to be rather easy to setup and get going. More can be found on the
http://opensourcecms.com/ website.
If you're looking for a blog-type system, then there's e.g.
Wordpress. It's very popular and there's loads of themes and plug-ins available for it.
Pixelpost isn't too bad if you're looking for a photo blog either.
Again, more of them can be found on the
http://opensourcecms.com/ website.
If you want
a solution in Flash, try these:
Simpleviewer
Flash Gallery
Art Flash Gallery
Flash Image Gallery
I don't like them, but some people love their flashy looks.
Offline gallery generators:
Jalbum - this one's quite popular. There are similar programs, e. g. in Python, but they're not as fast to install (you will most likely need a few extra things to install before it runs) and their templates are generally... pretty ugly.
Namu6 - it's more of a personal website editor, but if you don't have many photos, it can serve you well.