A few weeks ago Google released a new feature for Gmail called Priority Inbox that automatically determines which e-mail that you receive is important and filters those emails into a view. I think that Priority Inbox is the best feature that Google has added to Gmail since it launched, and I really hope it quickly comes to the version of Gmail on Android. Until Google adds Priority Inbox to Android Gmail, I have found a way to take advantage of it on my mobile phone by using the Gmail mobile web site.
When you load the mobile version of Gmail on an Android phone tap the Menu button to expand the list of Gmail labels. Gmail adds a label to the e-mail that you receive that it thinks is important to you, and you can filter your e-mail to only the important ones by selecting the Important label. (Note that this will also work on other mobile phones.) Ironically, I have never really used the Gmail mobile site on my Android phones because I think the Gmail app is great, but Priority Inbox has given me a reason to start using it.