Sorry for such a broad question. Part of the problem is that I don't really know what all these devices (calling them 'phones' just doesn't do them justice) can really do. A friend keeps showing me the amazing things his smartphone can do.
For instance, the other day (my friend and I) wanted to go out for lunch. He pulled up a list of restaurants near where we were with ratings and user reviews. Then once we picked a place, his phone told him how to get there. Then we got there, he pulled up an app which showed him the most nutritional stuff on that restaurant's menu. Then when one of his kids started getting a little unruly because he was bored, he pulled up an episode of the kid's favorite TV show on the phone and handed it to him. Afterwords, the phone calculated how much he should tip the waitress and gave us directions back to his car.
Before our lunch the main things I wanted a phone to do are the same things I'm doing now with my Pearl, because that's all I really knew that Phones could do. Stuff like Text and Call, Surf the Web, Keep my Calendar updated, Update Facebook, listen to Music (though many mp3s will not play on it, complains I don't have a license even though I ripped them from a CD I own). I use it for Navigation on trips, and jot down notes. I'd love to be able to sync my calendar with my wife's LG flip phone, but I haven't figured out how to do that.
Now I'm a huge NFL fan and I'd love to watch live games on my phone or catch shows like Total Access from NFL Network. During the season it would be cool to have my Fantasy league scores updating as I'm watching the games.
Edit: I'd love a way to show off my pictures from Facebook, or just random shots from my computer on my phone. My friends phone has the pictures take up the whole screen and they look really good. Also I'd love a way to put my Bible into my phone with a way to take notes, or underline stuff, but I can always pull that up on a webpage.
I was also afraid of the app list when I got the Droid, but so far everything I search for in the market, I end up finding, and also end up downloading a few other things I didn't think of, haha.
I have to say, though, widgets are awesome.
It's kinda like an app that gets displayed on your homescreen. It can display numerous things. Usually an app just places an icon that launches that app. Now a widget takes up space and can do things without having to open the app.