Can i build my own Realty website using Free yahoo or earthlink ? Or anyone can recommend me a good sites ?Would appreciate it thanks

Nothing worthwhile is free. I have mine on Yahoo associated with my domain name. It's not expensive, but is hard to set up.

If you're talking about hosting you definitely are better off with a paid solution. If you're talking about site building learn at least some basic HTML and you can do it yourself for free, there are even free PHP based scripts available for free as long as you understand how to work with it. For MLS feeds and things like that a lot of time your MLS will allow you to use their info you just need to ask (usually pay).