Even for short visits, seeing most of Berlin is a perfectly manageable. The subway is unimpeachable and bike thoroughfares, in typical German fashion, are all thoroughly and safely marked. Buses can be pretty much ignored for those who don't mind a little extra cardio, though night buses and taxis can be ideal for those times when the bike, for one's own safety, is best left for next-morning pick-up.
Though lacking the infrastructure of a city like Amsterdam, Berlin is more amenable to biking than most metropols. With wide streets, bike lanes carefully marked, and generally conscientious drivers, there is no better way to see the city than on two wheels. Follow the former path of the Wall, visit one of the many lakes within they city-limits, or push all the way into Grunewald. Find a German-speaker and sign up for Deutsche Bahn's Call-A-Bike program, which offers subscribers free touring bikes stationed around the city.
Berlin's U- & S-Bahn reaches every imaginable part of the city, though depending on it alone does not mean there will still not be occasionally demanding foot travel. The tickets are also not the cheapest, but always cheaper than being caught Schwarzfahren ("riding black"), which costs the culprit now a hefty 60 Euro. And no, you can't get away with not validating your ticket and claiming ignorance: Berlin's increasingly ubiquitous plainclothes ticket-checkers are ruthless. For the bikeless and short-term tourists, the Berlin WelcomeCard is the most bang for your buck. Bikes can be taken in the marked subway cars and cost an extra 1.80.
The buses run as well as the metro but are really only necessary for those who are traveling after 1 am or have no desire to walk at all. For those without bikes, or those with bikes but otherwise impeded, the night buses (the N lines) will be essential. They follow the route of the U-Bahn and generally come every 15 minutes.
Uber is as present in Berlin as any other city, and there are always taxis on the streets, especially near the clubs. Renting a car, unless the traveler wishes to explore outside the city limits, would be as much overkill as it would be in New York City.