They do, of course. There's the GmbH ("Corporation with limited liability"), which is pretty much exactly like a LLC. Recently, they also added the UG ("Unternehmergesellschaft") which is the same thing save for less statutory base capital.
But, as seems to be usual in Germany, everything is more complicated here. To found a GmbH, you basically need a lawyer and a notary. Oh, and 25k€. AFAIR founding a LLC is easier. However, thanks to the EU, you can of course found a UK Limited (Ltd.) with relatively little trouble.
In theory you can use a sample contract and found without a notary, in practice I have never seen it done and people I know used to recommend against it, but I haven't checked in a while.
Don't believe everything a random pundit on the Internet says. Yes, Germany has something like a Limited Liability company, since recently even without any required capital (beyond 1 Euro).
