It is possible to install the game on another computer, but there are a few things to keep in mind:
1) EA games frequently track how many computers they are installed to and limit them. The Sims 2 might be old enough that this isn't an issue, but just to be sure don't install it on all your friends computers. ;)
2) In order to save your houses and families, you must move the save game folder to the new computer. On a PC this will be located in your Documents folder, in the "EA Games" folder. The folder is called "The Sims 2" and you want to move the entire folder to some kind of moveable storage. I'd use a thumbdrive. After fully installing the game on the new computer, you can delete the automatically generated "The Sims 2" folder in the same location and replace it with the one with your saved game.
3) Corrupted save games can make your game very slow and freeze or crash. Before blaming the problem on your computer, try moving your current save to another location (like to your desktop) and load the game up without it. It will take a little time to regenerate the save folder, but see if the game runs better without your existing save. If the game runs better that way, you can delete the replacement files and try putting your old save back, but before you run it be sure to go into "The Sims 2" folder and delete the Groups.cache, Accessory.cache and cigen.package files. (Those three files will rebuild themself and removing them won't hurt your save. If it plays better with them gone, you won't necessarily have to start a new neighborhood/save.)
4) Maintenance you can do on your own might help your current computer run better for all programs. Download and run CCleaner Free from here: http://www.piriform.com/ccleaner/download This program removes unnecessary files like stranded temporary and cache files. Defragment your computer (assuming you are using a ATA/SATA hard drive). If your hard drive has less than 15% free space (your defragmenting program will give you a warning if you do) find items you can remove from your computer, putting them on disc or another hard drive.