i toook off the side case on my tower and i was wondering if it would be better if it left it on.. since i have a fan and it would make it better for cold air to stay in..

Im not exactly sure, i guess it depends on the computer setup. You can check with a temp monitoring software like speedfan and check temps with it off and with it on. Personally ive noticed lower temps with the case off when i had no case fans. But recently i got a power supply with 2 fans, and have added 4 case fans. Since ive created a strong airflow through my computer, taking the case off would disrupt that flow and make the case fans pretty much useless, i see lower temps with the case on and all 4 case fans going.

Leaving the side of the case off will expose the inside of the machine to foriegn bodies and makes a terrible racket. Modern cooling is designed to run with case on, and I believe - although Per may jump in and correct me here - that modern cooling is designed aerodynamically to assume the cover being on.

ATX and BTX standards assume a closed environment, will ventiliation being at specific points.

Moreover, with the case cover off there is no vacuum created by imbalanced fans. However, you are also rendering your case fans useless. They are simply moving air from directly outside the case - and right back out again. And, as mentioned above, having the case cover off exposes the computer to many potentially bad things such as liquids, flying objects, pets, fingers and more dust.

I would not suggest leaving the case cover off unless you had a fairly decent reason for doing so.

My hamster could use a death maze trap. :) Seriously, my ex-roommie found a pet snake in his VCR one day.

Close it up at least when you're done using the computer.