I got Weather Bug Elite because I like that it can detect my location and give me the weather for there along with weather alerts. I like real time radar as well. Many of the apps do that as well, but WBE had more of the options I wanted. WBElite also has webcams you can view as well as video weather reports for your region of the US - sort of like the "Weather on the 8's" from the Weather Channel.
I used MyCast Weather on my old LG Dare and wanted that but they didn't have it for the Droid until recently. So I purchased that as well because that has hurricane info as well (which WBElite and The Weather Channel do not - under Severe Weather). Right now it's tracking TS Estelle & TD Colin. Since I live in coastal Georgia, I like the heads up for that.
It includes a map listing all the alerts. I can see coastal flood watches in Miami area, as well as flood warning and heat advisories in the MidWest and Marine warnings in Louisianna. It also includes a sections called "Weather Fun" which includes a quiz type game played against other users, and some other neat little trinkets. But all those are secondary. I know the old LG Dare version had a lightning strike map in it as well but I don't see that right now.
I've also used "radar now", AccuWeather, Weather Channel Weather Widget, and the default weather widget that comes on the Droid. All have their advantages and some may have other options that might work better for you. It doesn't hurt to try a bunch and see. Even the paid ones since you can get your money back within 24 hours if it doesn't suit you or gives you problems.
I used to use Weatherbug (loved having the temperature in the notification bar) but am now using a combination of Beautiful Widgets (and the live wallpaper) and Rainy Days for radar. Sadly, the only thing I don't get is weather alerts.