The practice of not carrying a valid ticket for travel on the MVV public transport is known as Schwarzfahren - literally translated this means "travelling black". There is little excuse for travelling without a ticket. Arguing with the MVG ticket inspectors is a waste of time because they've heard all the excuses before. Sometimes, if you do have a genuine reason for not having your ticket on you - for example if you have a Jahresabo (a yearly ticket with your name on it) and you left this at home that day, well you can take this to the central office and your fine will be revoked. Other excuses such as simply not being able to understand which ticket you should buy so you bought none - this will not help you escape the fine.
The fine for travelling without a valid ticket is currently €40.
Each time you are caught your name and address is recorded. If you are caught multiple times within a certain timeframe the MVG may decided to prosecute you in court and land you with a much larger fine. The exact rules are not known but rumour has it that if you're caught three times within a year the fine is €1,000.