How do I see which applications are running in the background ?
How do I close some of those if I choose to ?

Wirelessly posted (Verizon 8830: BlackBerry8830/4.2.2 Profile/MIDP-2.0 Configuration/CLDC-1.1 VendorID/105)

Press the ALT-ESC button and then click on the open app and close it from there.
The most common app that I need to go back and close is the media app.

However, certain apps cannot be closed and will always remain running such as phone, e-mail. browser, messenger programs etc.

Yeah, seems media player opens 2 apps when listening to music or watching a video. The "Media Player" app is open, along with "Now Playing." If you just escape out, one of these will usually still be running in the background.

I've also found brickbreaker open a lot of times when I thought I've closed it. For some reason when you press the menu key will in brickbreaker, there are 2 "close" items in the menu. Seems the top item is the one that actually closes it. FYI