Gmail for iOS is the official e-mail client from Google for iOS, and it's mostly a solid offering with only a couple of issues. The initial release got off to a rocky start with notification errors, but a subsequent release seems to have ironed out the major problems.
Obviously, the Mail app that comes with your iPhone lets you connect to Gmail accounts, but with the official app from Google, you'll get a few more options that you may have come to rely on when using Gmail. Get started by creating a new Gmail account or logging in to your current account. Once logged in, you'll get a view of your inbox with a Menu button in the upper left, and Search and Compose e-mail buttons in the upper right.
As you would expect, Gmail for iOS has most of the basic tools found in the browser-based version. You can read mail and browse through threaded conversations, keep track of important messages in a priority inbox, and you can organize your mail using starred messages, labels, and archive features. Also, Gmail for iOS gives you notification badges on your home screen when you receive new mail. Other features include autocompleting contact names as you type, the ability to send and receive attachments, and Gmail's excellent search functions.
Our only issues with Gmail for iOS so far are that you cannot zoom in to your inbox to read the small type (a simple pinch to zoom feature would fix this), you can't create labels from within the app, and, more importantly, you cannot select and copy text from message windows. Not being able to copy and paste text is a huge oversight (think of copying an address to get directions in the Maps app, for example--an extremely common occurrence for many), so hopefully Google will release an update soon to fix these issues.
Overall, if you're a Gmail user who likes Google's features for organizing e-mail, the official Gmail app is a good option with only a couple of problems. Hopefully future updates will fix the minor issues and make the app a complete Gmail client.