I use AndroZip for my file manager. I like the fact that, in addition to the usual file-manager stuff, you can create or unpack .ZIP files (and .TAR files). Not sure if most other file-managers can do that or not, because I tried AndroZip and liked it right off the bat. Never used another file-manager app.
Other free apps that I've installed:
SportsTap (keeps track of your favorite teams, NFL, NHL, MLB, NCAA, NBA, etc., etc... Pops up notifications when scores change.)
Battery Widget (a power-management widget that takes up only one single spot, rather than 4 like the built-in one)
Talk To Me (a translator -- speak English, and the phone translates and speaks the language you selected.)
WiFi Analyzer (awesome tool for checking which WiFi Channels are in highest use, or how good/bad the local WiFi signal is)
SleepTimer (automatically shuts off Music Player and/or WiFi after a time limit that you select.)
The Weather Channel (widget that shows up-to-date weather data on your home screen)
WaveSecure Beta (if your phone is lost or stolen, this will lock it down, and allow you to erase it remotely.)
MotoTorch (uses the Camera LED as a flashlight.)
Google SkyMap (Shows you the position of the stars and planets, based on your current GPS location.)
RealCalc Scientific Calculator (SOOO much better than the built-in calculator).
Barcode Scanner (Scan barcodes of just about any sort. Easily transfer contact info, too, via bar-codes on the screen.)
Games that I've installed (both free and paid):
UNO (the classic card game -- well done, although not quite perfect. But they're issuing updates regularly. Paid app.)
Solitaire MegaPack (36 different solitaire games built-in. Works perfectly. Paid App)
Sudoku Free (Name says it all. It's Sudoku, and it's free. Premium version is available if you want to donate to the developer.)
Jewellust (Ever played Bejeweled? Same game, different name. I think it was a paid app, but I can't remember offhand.)
Best thing to do, though, is spend some time in the Android Marketplace. Look around, read the reviews of anything you think you might like. There's usually a 'Lite' version of any paid app so you can try it out for free first, before you go spending your money. (And if you uninstall a paid-app in the first 24 hours, you automatically get a refund).
Also how should I manage folders on my home screens? I'm still not sure what to do there?
What I've done, is created folders on the main home-screen, that say "Phone", "Internet", "Utilities", "Games", etc., etc... Then I drag (long-press puts you into drag mode) the icons from the Applications Menu into whatever folder I want them in. This leaves me plenty of room on my main home-screen for The Weather Channel Widget, the SportsTap Widget, and the Google Search Widget.
To create a folder, long-press on a blank area of the screen and select Folders, then New Folder. To rename the folder after it's been created, open the folder and long-press the title-bar where the name of the folder is. It will then ask you for the new name.
But the best thing, by far, about the Droid, is you can customize the home screens ANY WAY YOU WANT! You can put the folders/shortcuts/widgets YOU want on there. Play around with it for awhile... You'll see just how amazing this phone can be -- as you use it, you'll see which apps/widgets are most important to you, and you can put them where you feel its best to have them.