I just got a new computer and am in the process of moving my game onto it. I've installed all the games, copied over my neighbourhoods and custom content. I'm just wondering if I need to click on the sims2pack icons in my downloads folder and reinstall them or if doing so will cause me to have doubles in my game.
Thanks!

Erm. Do you keep sims2packs AND their content in the Downloads folder?

The only content from sims2packs which does not go into Downloads folder is lots (lots themselves, CC packed along with lots goes into Downloads still). Lots go into Teleport and then game "teleports" them into LotCatalog. Hence it's easier for you to save LotCatalog folder along with Downloads instead of reinstalling sims2packs.

Having sims2packs in your Downloads folder is pointless - they won't show up like that. When you double-click a sims2pack, with the exception of lots, it's turned into a package file (or several package files) and put into the Downloads folder. So, if you've already installed those sims2packs in the past by double-clicking, then the package files from them will still be in your Downloads folder and you don't need to install them again. If not, then the sims2pack CC will never have showed up in your game in the first place, so you probably won't miss it .