As a web developer I enjoy contributing to projects that help me to identify stupid things, because there is an abundance of stupid in web technologies. I enjoy contributing to things like JSLint and Pretty Diff.

Sometimes contributions can be as simple as bug reports or feature suggestions. This kind of information is golden for complex projects maintained by very few individuals.

If you are a javascript developer than you can start with libraries available on Github. I started with a small plugin called jPulse, few days back i sent a pull request to an yeoman plugin. Easiest way is by looking into the projects that you use yourself, that way you will have an understanding of how everything works, and you will be in a better position to contribute

I'm not sure what languages you know, but WordPress is a great one if you can program in PHP. The code is easy to read and there's plenty of room for contributions and improvement in WordPress core. Also the community is really friendly and welcoming.

There's even a list of "Good First Bugs for New Contributors": https://core.trac.wordpress.org/tickets/good-first-bugs

Yeah, I've heard great things about the Wordpress community! Some of the others that I've found have a great support base are Open Streetmap, Open Science, and Ubuntu.

The best is start with what you use, and are passionate about.

I started with Mozilla, then moved on to OpenBSD, FreeBSD, *BSD.

Find something that you love, with a part that annoys you, fix it, see how it goes.