Google officially announced a beta program to offer Gmail for Domain for companies which need the service by filling up the form available at https://www.google.com/hosted/Home. Google is also now an ICANN-accredited registrar of domain names.
Yahoo has been offering the services for quite a long time but I still find that Google Gmail is more easy to use and much faster. Many Internet users has signed up and use Gmail for their personal use. Introducing Gmail for domain will increase the usage of Gmail services and many small and medium firms will surely adopt the Gmail services with Domain.
Google has been offering Gmail Solutions to San Jose City College and their login screen can be viewed HERE
Microsoft has also been offering the same service via Microsoft Live but again the Web Email interface is not as attractive as that of Gmail. As the way it go, Google will likely win the keen competition in this area.