What do you need in terms of space/bandwidth/features?
IMO there are loads of extremely low cost web hosts out there. Everything on the internet can't be free! Pay a quid or two a month and be done with it.
There follows some nerd stuff.
Alternatively for low bandwidth stuff, I run a webserver at home. My cable modem connection is 1.5mb down and 256kb up. The speed is ok unless you have a lot of visitors or loads of images. I dont recommend that you do that unless you know a lot about web servers and security.
I have MRTG running on my Windows 2000 box, it graphs the bandwith usage, connections to my WiFi access point, memory, disk space, yada yada yada....: http://1ud.net/stats/