I've been using lighttpd as a development webserver for an scgi based webapp I'm building. I was very impressed with its ease of configuration and automatic load balancing between scgi processes. Getting mod_scgi to work in Apache was a nightmare.
I haven't encountered any problems in my development environment, but it seems that it's no longer in active development (last release was August). The email list and forums are generally dead. Although this isn't itself evidence of a problem, inactivity seems to raise questions.
Several large-volume websites use lighttpd, so in that sense it's 'proven' enough. That said, development and/or community involvement has slowed down greatly after the original developer Jan Kneschke landed a job at MySQL working on other things.
The current favorite in the low-resource-requirements & high-speed HTTP server space is nginx (pronounced EngineX). Have a look at the recent stats (second illustration) -- nginx is a late entry on the charts, but it is growing fast and already well ahead of lighttpd in marketshare.
If nginx works for your needs, then I would suggest to use it instead of lighttpd; nginx is benefiting from more active development and more widespread use now (nginx 7.57% versus lighttpd 0.69% of top sites in the above linked Netcraft results).
There is ongoing development: http://redmine.lighttpd.net/repositories/show/lighttpd
There are also a lot of people using it. There has been some decline though, because nginx is much more hyped. There are also other smaller web servers which are similar to lighttpd, like Cherokee. I used each of them for a while, though just for personal use.
All these servers host serious web sites. You can find them on their wikis, etc. So yes, they are production ready. IIRC YouTube or a similar web site has been using a lighttpd setup for quite a while. Oh, The Pirate Bay is also a prominent lighttpd user.