What licenses are the best for open sourcing web applications?
The answer for the "best" depends too much what you hope to accomplish, so a concrete answer is impossible.
If you would like to know more about the types of open sources licenses and what they offer, Wikipedia is a great place to start.
It depends on your licensing goals.
- If you just want the code to be widely usable, MIT or 3-clause BSD work fine.
- If you want to require redistributions of your code to be under the same license, GPL works.
- If you want to require deployments of your web application to distribute its source code, with any modifications, then you'll need the AGPL.
If you are fine with your application being used as the basis for a proprietary web service, then just pick a standard license (BSD, GPL, MPL, whatever) using the same criteria as for other projects. If you want to prevent that, however, the only option I know of is AGPL, which requires that installations provide source to their users. Then BigBucksServiceVendor can set up an installation, tweak it, and charge users to use it, but they must provide their source code so that someone else can do the same as well.
The AGPL also, though, is not near as widely used as many of the other licenses. That may impact your decision.
Despite the multitude of open-source licenses, there are probably only a few you can realistically choose from when it all boils down. As Mike was saying, it all really depends on what you're looking for.
Realize that open-sourcing is just another form of license protection, so deciding for yourself the terms under which you want it to be released will greatly affect which license you choose. Do you want to allow commercial endeavors to profit from your work? What if someone were to modify your code significantly into their own derivative product... can they distribute it (for free or not) without also distributing the original or at least linking back to you? Do you care if anyone gives you credit at all for your work? These are just a few questions that should probably be answered before you head too far down this road.
I'd recommend taking a look at a few wiki pages -- specifically, investigate the difference between permissive and non-permissive licenses, as these are the two major types of open-source license. When you get around to figuring out what exactly you want to protect and how you'd like to protect it, that's when I think the right decision will become clearer for you.
There are a variety of options depending on what you're looking for. There is a very good article on Wikipedia describing many of the licenses and what it means to use a specific license.