The Weather Channel caused huge issues for me last time I had it. To be fair, that was over a year ago on a much older phone, but I have no reason to trust them now.
Dialer One is a nice alternative to the stock dialer. Dolphin Browser HD is a nice browser as well as Opera Mobile. Apps Organizer and Folder Organizer are a little bit nicer alternatives to the standard folders in Android. I use Handcent SMS instead of the stock messaging app. I'm a sports fan and I got a free (normally paid) app from Amazon called SportCaster Pro that is quite nice - gives you scores but also a running Twitter feed relating to whatever game you have pulled up, which to me is much more immersive than just stats. There's a cool app that lets you listen to just about any radio station in the country called TuneIn. I have an alternative alarm clock called Alarm Clock Plus that I like a lot, tons of options like configuring snooze time, gradual volume increase, and reading the time to you. Lastly I use Yelp a fair amount to find good local restaurants.