I'd shut down all clients connected to the account, goto mail.google.com, click the "details" link at the bottom right of the page and sign out of all other sessions.

Then start Opera Mail and try to connect. On the incoming tab in the account's properties though, make sure "check for new messages every..." is enabled and make sure it's between 9 and 31 minutes. This is to initiate IDLE and keep it from timing out and to keep Opera from connecting to the server too much.

Another thing it could be is that the server settings are wrong. Opera's new account wizard will automatically configure the correct Gmail settings when you enter your email address if it sees @gmail.com. But, if yours isn't @gmail.com, use @gmail.com in the account wizard to get the right settings and then change it to the correct @... later.

In Opera, did you choose IMAP or POP for the account type when you set up the account? If you used POP instead of the default IMAP, note that there are POP settings at mail.google.com that controls what happens when a messages is accessed via POP. If the message is removed from the server by another client, Opera won't ever see the message.