The German tax system is one of the most complex in the world. There are a lot of cases and exceptions that can be written off from taxes. Below I will give the most popular examples:
Work-related expenses (Werbungssteuer): The finance department takes into account a lump sum of 1,000 €. You can write off even more if you exceed this amount. You can write off your home office (€600 flat fee), your commute to work, part of the cost of your personal smartphone, laptop, telephone operator and internet, moving (€870 flat fee), just write off the €110 flat fee for petty expenses, work uniform, advanced training, work literature and much more.
Housekeeping services (Haushaltsnahe Dienstleistungen): Even if you didn't pay for cleaning or plumbing services, look at your utility bill (Nebenkostenabrechnung). You can write off the services of cleaners, a housemaster, a gardener, and even an elevator repairman from there. Usually such services are specially labeled as Haushaltsnahe Dienstleistungen for ease of calculation.
Child expenses (Betreuungskosten): if you have a child, you can write off child care services: kindergarten, babysitting and even train and plane tickets for grandparents.