Apps to save battery life -
Advanced Task Killer (there are many called this, but look for the one by Rechild) - Kills any unnecessary apps in the background
Y5 Battery Saver - Switches off Wifi in areas where there is no wifi signal, switches it on automatically if it can find a network you've connected too before.
Battery Minder - Tells you how much battery you have left. Also tells you how much time you have left.
Internet Stuff -
Dolphin HD browser - Could be better than the installed browser (although the installed browser is pretty fast).
Facebook - Just update the already installed app
Youtube - Again, just update the already installed app
Gmail - I have a gmail account, so this is pretty good for me, not sure if hotmail offer an app for android
Netcounter - Monitors your internet access, handy for watching if you're going to go over your allowance
Other Apps -
Angry Birds - Addictive game
Documents to go - Allows you to look at MS Office documents
Amazon Kindle - For downloading books etc
ES File Explorer - Allows you to browse the files on your phone as you would in windows
ES Security Manager - Allows you to block your phone via text message, also backs your phone up at the same time.
VLC Remote - Media Player that plays anything
Uninstaller - Uninstalls Apps which you no longer need as it's quite complicated to do so with out a dedicated app. Advanced Task Manager also does this too.
BBC News/BBC Sports/Sky Sports App - Just quick ways of accessing sports and news on the BBC & Skysports websites.
Camera 360 - An app for taking photos (better effects than the pre installed app, but there is nothing wrong with the app already on there)
Also an app called Barcode Scanner. Scans the barcode of items in shops etc and looks for cheaper versions online
You'll need an antivrus programme on your phone too.
Go here -
Top Android Security Apps: Antivirus, Spam Blocker And Anti Malware | areacellphone.com
Then look at the 3rd app down. Install barcode scanner, Open it via the menu and put the square picture thing next to the third app on the web page in view of your phones camera and it will install the application for you itself. Alternatively, just search for antivirus via the android marketplace. The scanner thing is cooler though.
Also, I couldn't receive MMS messages straight out of the box, I had to update the phones firmware. To do this, Press Menu, then settings, then scroll down to "About Phone", then Hit System software updates and then "Check Now", it's quite a big one so it's advisable to be connected to a wireless network when doing this.
With the amount of stuff on there, it seems totally daunting, but it's so easy to use it's incredible.