For PHP/MySQL:
http://www.phpwebhosting.com
For ASP/ASP.NET:
http://www.webhost4life.com (never used this one, but a friend recommends it highly).
Both are reasonably priced (~$10/month). PHPWebHosting.com's support is excellent.
Domain name registration is separate. Well, you can have the hosting company do it, but it's better if you keep them separate. I recommend GoDaddy.com or DomainMonger.com.