Can 'droid dorks play too? I think most of these are available cross-platform, or at least there are similar cross-platform apps.
I put my most-used apps on my main homescreen:
From top to bottom:
1. The HTC clock/weather widget (I don't have an HTC phone though) at the top, shows current weather and temp at a glance
2. RealCalc is a scientific calculator, similar to an old TI35
3. GSD - one of my apps for calculating flying height and specs for aerial photo jobs
4. Memo - simple memo book for jotting down stuff
5. AirWX - aviation weather, pulls up the current aviation reports/forecasts, pireps, and instrument approaches for airports
6. Garmin MyCast - satellite and radar weather images and general weather info - there's an aviation-specific one for $129 but I haven't seen the need for it
7. Weather Chan - obvious...about the best general weather app I've seen (weatherbug is good but it appears to want to download tons of stuff when it doesn't need to).
8. Google Maps - the quickest mapping app I've found and has google earth overlays that couple with the GPS. I use it to look at traffic conditions mostly.
9. On the bottom row the only special "app" I have is the Google Voice app - I use that for my voicemail
Others I use often are:
10. Barcode scanner
11. MapDroid - uses locally-stored maps (worldwide) instead of network based
12. Kindle - loads whatever kindle books I want to sync from my kindle
13. Adobe PDF reader
14. Google Sky
15. DroidSat - plots the current location of satellites and works as an aiming device so you can view them. I use it to watch the ISS fly over usually.
Hidden, but running are:
(1) a gmail notifier app - customized so I only get email updates on a specified schedule.
(2) I also have "tasker" running, I have that configured to automatically turn off the 3G portion of the phone when I'm certain areas that I use wifi - and conversely it turns off wifi when I'm away from those areas (it's based on the cell tower the phone is using). It also raises/lowers the ringer and notification volumes based on time and where I am.