The following list is meant for your general orientation. Most of Berlin's festivals and events take place in the same month every year, so the list below is sorted this way. Please bear in mind though, that some aren't locked on a particular season or month, so make sure to check the website of the specific event you're interested in.
The events might also be relevant for your visit in a different way: Hotel prices tend to go up during major international events that bring many professionals to the city, so you might want to check if your planned vacation overlaps with one of them.
The Berlin Fashion Week
The Green Week (Grüne Woche): Berlin's international food & agriculture fair
The Berlinale - Berlin's film festival is considered 3rd most important in the world (right after Cannes and Venice)
https://www.berlinale.de/en/HomePage.html
The International Travel fair of Berlin (ITB)
The Berlin Half Marathon
http://www.berliner-halbmarathon.de/en/
The Jewish Film Festival Berlin Brandenburg
The Gallery Weekend - a festival of contemporary art
http://www.gallery-weekend-berlin.de/
Berlin's International Theater Festival
https://www.berlinerfestspiele.de/en/theatertreffen
Carnival of Cultures in the very multi-ethnic borough of Kreuzberg
Fête de la Musique – a worldwide music day
http://www.fetedelamusique.de/en/
Christopher Street Day (Gay Pride Parade)
The Berlin Fashion Week
https://fashionweek.berlin/en/index.html
Classic Open Air
The International Berlin Beer Week
The Berlin Marathon
http://www.bmw-berlin-marathon.com/en/
Berlin's international Consumer Electronics fair (IFA)
The Berlin Art Week
Pyronale, "the world fireworks championship"
The Festival of Lights takes place every year in autumn. The city's architectural milestones are illuminated with special designs and colorful decorations:
http://festival-of-lights.de/en/
Christmas markets, and plenty of them! Some of them in "typically German" tradition:
http://www.visitberlin.de/en/experience/wintertime-in-berlin/christmas-markets?tid=3289
Louis Lewandowski Festival of synagogue music
https://www.berlin.de/en/events/2819212-2842498-louis-lewandowski-festival.en.html