A number of users are reporting problems accessing Gmail on their iPhone or iPad.
According to AllthingsD, users have been receiving error messages along the lines of "mail service imap.gmail.com is not responding" when trying to log in to Gmail on their iOS devices.
Google is apparently aware of the issue, and in its Gmail forum, a company representative has tried to offer users a work-around:
We are aware of the issue and we are working to resolve for the accounts affected.
For users that may have joined this thread after my posts (they are at the top), you can still check your mail through your computer's Web browser. If you're having trouble on your mobile device or tablet, you also use the device's browser or for iOS and Android, download the Gmail application.
I know this isn't your first choice, but it will allow you to continue accessing your messages in the meantime.