That really depends on what kind of LLC you want to open. There the so-called "UG Haftungsbeschränkt" which was created as response to the British Ltd. and costs somewhat less than 200 Euros + whatever capital you want to invest. For larger enterprises, you'd probably found a GmbH which usually costs somewhere between 1000 - 2000 Euros in Legal Fees [1] and needs a minimum capital of 25.000 Euros (which you can use to pay the legal fees, so you don't need those extra). The costs of creating a business in germany are probably not higher than anywhere else in Europe.
[1] as always, legal fees can be significantly higher than that depending on how complicated the case is.