Activation is a completely different process from windows installation. And this process is different in different versions of windows so you would have to see which windows you have here. I will explain for 3 majorly used windows.
First of all, all these 3 windows have a grace period or trial mode for 30 days. After that activation by purchasing a genuine key is necessary. For Windows XP, if the system isn't activated in 30 days then one won't be able to use windows after that. Only thing afaik is that one can make backups or activate it to gain complete former access.
For Vista, it gets a bit worse. After 30 days when the user doesn't activate it with a genuine key, vista enters in the RFM mode. Which is Reduced Functionality Mode. Wth is this? Well under RFM one can't play windows games & premium features like aero glass, bitlocker and ready boost etc are disabled. Another annoying thing is that after every hour it will log you out automatically which can be a bit frustrating, especially, when someone is doing some important work on it.
For Windows 7, it's not much of a hassle. Here you will only get annoying prompts that the copy you're using is not genuine or the software is counterfeited, if one tried to use a crack etc, which is illegal. One won't be able to update its windows any further which is essential since updates often provide several essential things which might improve performance or upgrade security or close any existing exploits which hackers always try to find and take advantage of.
Common example lets say an update of MS programs like Internet Explorer or MS Office etc. No free updates for a cool program like MSE (Microsoft Security Essentials), which is a capable free antivirus. Another thing is that you won't be able to set desktop backgrounds permanently to your preference and it will constantly set itself to black screen every hour and remind you on the bottom right that it's not genuine etc. Unlike Vista, here performance wise you won't lose anything, though, as stated previously you have a lot to lose if you can't have updates anymore.
Hope that amply answers your question.