Can I apply for British citizenship and still keep my EU passport / nationality?
It depends which is your EU country of citizenship.
Some countries, like The Netherlands, Austria, Spain, Estonia, Lithuania, Latvia, Slovakia, Slovenia and Germany, have restrictions on dual citizenship.
Others, like Romania, allow dual citizenship with the UK for all their citizens.
the3million Young Europeans have created a document which gives more detail: http://www.t3m.org.uk/t3m_YE_BarriersToCitizenship_DualCitizenship
These rules are also currently debated in some countries and they may change. Before applying for British citizenship, do check with your embassy or consulate about your EU country’s rules on this issue.