The Wooden Simolean

IMHO, reinstalling is pointless! Yeah, it'll get your game running... then you'll put your backup back in... and the game won't work again, because the problem was in the My Documents/EA Games/The Sims 2/ folder. Or you've lost all your neighborhoods and downloads and get to start over, because you didn't make a backup. If we wanted a game that you have to start over, we'd play a First Person Shooter, not The Sims! 

Errors hardly ever affect the files in Program Files/EA Games/The Sims 2 (etc.), with very few preventable exceptions.  Follow my tutorial on preventing file corruption, and you should never need to reinstall again, since the game cannot corrupt its own files after this.

First diagnostic method: Go to My Documents/EA Games and rename your The Sims 2 folder to something obvious, like The Sims 2 Safe Place.  Reboot  your computer.  Run your game.  If the game runs, it's something in your neighborhoods or custom content; keep following this tutorial.  If the game crashes, you need to reinstall, but your 'hoods and custom content are mostly in a safe place.  Only your Scriptorum files need to be backed up.

Most likely really corrupt files: accessory.cache, groups.cache, and cigen.package Suggested fix: go to My Documents/EA Games/The Sims 2 and rename groups.cache to groups.cache.bak, and similar file names. Run the game. You'll be surprised at the number of times this fixes your game! And you've got your old file on the odd chance that it was something else.

Next most likely corrupt file: NeighborhoodManager.package This file can be deleted without harming your game in any way. Apparently the game ignores it except to crash if it's corrupt.

Third most likely corrupt file(s): Thumbnails folder  If you delete or rename the whole folder, the game will copy the thumbnails from the game files, then add the thumbnails for your custom content.

Fourth most likely corrupt file: Exported Sims in SavedSims   Maxis premade Sims are notorious for this.  If BodyShop will still run (a sure sign that this is the problem), resave exported Sims and delete the original exports.  If BodyShop crashes or hangs as well, drag the exported Sims out of SavedSims and run the game or BodyShop again.

Fifth most likely corrupt file: Something in Downloads  This is a little tedious to track down, but here's a tutorial from the MTS Wiki for the 50-50 Method.

Beyond that, if your computer crashed during a save, it might manage to corrupt real files in My Documents/EA Games/The Sims 2. You can simply rename that folder and let the game create a new one. You can even attempt to salvage your old 'hoods and Downloads if you like once you have a functional game again.

Miros' #1 Rule: Don't delete! Just drag custom content out of your game!
Reasons:
1) It's probably perfectly good, so why delete it?
2) You might not be able to get another copy of it, so it could be gone for good...

Now for my recommendations on what to do:

Do make backups.

Do write protect your files!

(Written so I don't need to keep retyping the darn thing every time someone says why do you tell people reinstalling is pointless?)