If you are new to android, the menu button, and also a "long click" or "long press" are similar to the windows right mouse button, and give various options depending on the app you are using at the time.
Some of our favorite free apps are listed below.
You can get them at the android market.
Go launcher ex - totally change the look and feel of your android device and have much more control over it.
Android assistant - great task manager and system tool, quickly free up memory and much more.
AVG antivirus - free and works unobtrusivly in the background.
Scansfer - You will be amazed at the things this app can do
Dropbox - Access your files anywhere
Cool reader - ebook reader, supports most formats
ebay - Do your ebaying from your phone or tablet
first aid - hope you don't need it but if you ever do it could be a life saver
Mobile web picasa - manage your pics locally and on line
IMDB - internet movie database
Paypal - like it says
QuickPic - fast picture viewer
More to come, let me know if you have any you think should be added to this list.