Not if you're domain registrar is GoDaddy. Joke, but really it really depends on your needs. Are you going to use a lot of bandwidth? If so, you'll want a robust host that specializes in web hosting rather than domain hosting.

If you're looking to do some mini-site development, you might want to try:

http://devhub.com

Free, easy to setup a custom site, and pays even if your mini-site earns just $5/month.

Yes you can host your website with your Domain name provider.I have registered domain name and hosted my sites at same provider named as http://www.9cubehosting.com/ They provided me many free services with domain.The service and support is really Good.