I still had a an old flip phone, one I'd used for about 10 years, much to my computer-geek son's dismay. He finally talked me into upgrading--I tried a Blackberry, but like you, I just didn't much get the point. He finally got me to switch to a smart phone in March; I got a Samsung Galaxy Droid, and I am Addicted! I had NO idea I would use it so much. I was afraid it would just feed my FB addiction, but I rarely use it for that.
The apps I use the most:
Amazon Appstore--has a deal of the day where you can pick up some decent apps that usually cost money for free.
500px Land--an app to browse the photos on 500px.com
Kindle app--where I've downloaded several of my camera reference books, so I have them "on the fly"
YouVersion Bible App
Calendar--I use both a Google Calendar and one called Business Calendar
Camera apps-- Camera Fun Pro, Camera360, PaperCamera, FXCamera, Little Photo, Photoshop Express
CamScanner--allows me to scan receipts, papers, etc instead of stuffing them into the black hole I call my purse
Google Docs app
Dropbox
Evernote--allows me to sort notes, drawings, and pictures all related to different projects and keep them together
Flashlight app...seriously, I use it all the time, lol
Google Goggles
Layar--my son downloaded this (and most of my apps!) and I thought I'd never use it, but it's awesome
Mobile Metronome
Musical Pro--I am taking music lessons from our choir director and this and the metronome are invaluable to me
My Fitness Pal--keeps track of my exercise, my diet, everything
ESPN Scorecenter
Shortyz--Crossword Puzzles
SoundHound--LOVE this!!
Stopwatch/Timer app
Sundroid--tells you when sunset, sunrise and all the "stages" of them will be that day (civil, nautical and astronomical)
Urbanspoon
WeatherBug Elite
Believe it or not, there's actually some I use a good bit that I left out! These are ones I use at least once a week. I did leave out ONE I use way more often than I should, but I'll just admit...I am addicted to Angry Birds. It is the dumbest game ever, and I can't stop playing it...