To cut off the inevitable torrent of conflicting advice, the basic reply is:
- yes it's possible
- yes it depends upon what your email service is (as you generally don't want to receive them on your computer THEN forward them to your phone, but you'd like to receive a copy on each device)
So, the 3 questions you need to answer are:
1) is your mailserver running POP or IMAP?
2) what's the part to the right of the @ sign in your email address?
3) do you use Gmail on your desktop?
EDIT: Not that BOAC's questions weren't valid - we just need some info from you before suggesting (but I predict some people will try to reply with their experiences without knowing your circumstances).