The story so far:
what else is out there?
etc...
If you are not Microsoft-hater, you may also look into http://www.codeplex.com/ However I have not used it yet. Plus it uses MS Team system as source code control system hence it'll be an added advantage if you are developing .NET apps using VS2008.
But personally I prefer Google code. It's quite straight forward and easy. Also it is quite fast for updating / committing the code. Hence I recommend Google Code.
This Wikipedia article and this page list the alternatives and compare features.
SourceForge is ok, but their servers are slow as hell (I imagine they get a lot of traffic), and none too pretty. If you want to user their webspace, you're restricted to PHP4.
I haven't tried Google Code, but I saw on the website that you can only host up to 5 or 6 projects there, so that was a dealbreaker for me, since I want every one of my projects to have its own project page.
I switched from Google Code to Assembla for my project. I'm using their Git repository. Has worked well. I'm particularly fond of their hierarchical ticket system. There has been only one outage ever, that I've noticed.
From personal CodePlex experience:
Note that the above was written before the recent (as of 2008-01-14) major overhaul of their website. Some things have changed considerably, e.g. the code repository browser. I can no longer judge what disadvantages this site has to others. I don't delete this answer since the “pros” are IMHO still worth mentioning.
From a source administrator's perspective, CVSDude have an open source plan. I have paid plan and I think they're amazing.
From a user's perspective, out of all the web-based repositories, I prefer getting code from google code.
I also used Assembla for a couple of projects. Never had any problems, and it also allows you to upgrade your free space to a commercial closed one later, which can be useful if you're working on an personal project and want to have a repository accessible from anywhere.
Depends on what VCS you use.. If you use git, or you don't have a specific one in mind, I'd recommend git and Github. Or if you want to use an open-source site, Gitorious. Git allows people to contribute to your code very easily (infinitely easier than with SVN, not too sure about Mercurial as I've never really used it)
Launchpad seems to be a good Bazaar host.
Google Code is probably the best SVN host, CVSDude do SVN hosting which I used for a while, and they do CVS hosting (obviously), if for some perverse reason you want to use that..
I've used google code and launchpad mostly, and occasionally looked at sourceforge.
Sourceforge does not seem user friendly, has not moved on in ages, and I would avoid for a new project. Update: Sourceforge has recently launched support for git, bzr and mercurial, along with running your preferred project management software - trac, mantis etc.
Google code is pretty nice. The code browsing is good. There is a nice wiki to document your project. It uses subversion as its VCS so is well supported by many tools, good integration with IDEs, and the other advantages of a mature tool. Update: Google has recently decided to add support for mercurial.
Launchpad is cool, the major missing feature being some sort of wiki for users to document their project. It is developing fast (a web API has just been released) and uses my favourite VCS - bzr. And for those it matters to, the code for launchpad itself will be released in 2009, so you can run your own instance if you want.
As to how to choose, I would start with the VCS you want to use, and then choose from the hosting choices available. I won't go into VCS choice on this question ;-) (If you want to then check out these questions.
@dbr: launchpad uses bzr, not mercurial.
For mercurial I can recommend bitbucket and freehg. Bitbucket has a nice clean web interface and includes an issue tracker. The downside is that you can only have one free repository up to 150MB.
Another vote for google code.
The only downside is its mostly-text-only UIs.
Other than that it's awesome.
I've been using Assembla for my personal projects & it's brilliant. Its modular approach which lets you use just svn, or just the todo-list or you could use its trac server to do everything.
The only problem I've found is that it can be a bit slow at times, but it's not ever been an issue for me