If you did not register as “Kleinunternehmer” you will in most cases have to show VAT on invoices if your customer is located in Germany.
The most frequent domestic case we come across in which a VAT exemption applies is teaching income (if your customer is VAT exempt).
If you provide a consulting service to a non-German VAT registered business within the EU you will almost certainly not have to show VAT. To qualify for this exemption you need to make sure your client provides you with their VAT-ID. To check whether their VAT-ID is valid you can use an online tool at www.ec.europa.eu/taxation_customs/vies/vieshome.do?selectedLanguage=EN
If you provide a consulting service to a customer outside the EU you will also almost certainly not have to show any VAT on your invoice.