I am another that closes apps after I am finished with them.

However, when the phone is not at rest:

-Conversations - IM enabled
-phonebook (as a way of quick firing SMS)
-Media Player (with FM transmit when in car)
-Email
-Some game or other (when not in car!) This will stay open if level is not complete.
-I'll flick in and out or Phone App and Conky as and when I need/am interested
-Same with web - one or two browser windows checking links from email and facebook.

Plus others will come and go so I guess 3 Permanent and up to 6/7 one I get going.