I've recently encountered this after replacing the HD in my computer. I was able to copy the apps from my iTouch onto my PC.
Provided iTunes on your PC is using the same account as it was on the other PC, apps you have already bought should be able to be downloaded again for free-- that is if you choose to buy them from iTunes again, it should say you've already bought it and allow you to download it again for free (useful for any apps you have deleted from the iTouch but would like to reinstall). The only downside is that you won't know if iTunes will let you download it for free until you try-- it will still show up as costing the normal price, and only when you buy it will you be told that you've already bought it so it is free to download again. That's rather naughty on Apple's part because if you are at all unsure about what you've bought, there's no way to tell if you will be allowed to download it for free, or be automatically billed with no way of avoiding it.