Most, if not all EU countries have provisions for obtaining citizenship after a certain number of years of residence. Or do you mean gaining citizenship after a certain number of years in any EU country?
Yes. Like in germany, where it takes about 16 years of living there to get a citizenship, and since you were not born there, you will always be a second class citizen, always. Plus in a typical racist/ethnocentric way, you have to renounce your motherland's country's citizenship. No, thanks.
There is a real good reason USA attracts smart immigrants in droves. Even with the latest problems after 2001, this country will be able to attract more foreigner than any other country in europe.
Permanent residence is a load of paperwork, but still fairly straightforward if you've been working in Germany for 5 years and as of the latest laws gives you the right to work and live anywhere in the EU.