Assuming you can handle the Japanese to make a phone call, or your hotel concierge will for you, it's a good idea to make reservations for popular bars. Although there are figuratively tens of thousands of bars in Tokyo, they often only have a few seats. The population density here means that those seats will fill quite quickly, so you'll be turned away. Online reservations have not caught on in Japan, especially at the high end.
Reservations are especially useful if you plan on going on a Friday or Saturday night, since like everywhere in the world, people tend to go out these nights. For more advice on what nights are good in specific neighborhoods of Tokyo, see our Night Out guides.
Most cocktail bars will open around 5-6PM for aperitifs and close around midnight, and 8-10PM is prime hours since many people will have eaten dinner prior to drinking cocktails. And you probably should too, says your liver.
All that said, many bars simply do not take reservations. Other bars do not take reservations but may hold seats for your for 15-30 minutes if you call and ask.
Whiskey Richard is the founder of nomunication.jp, and has been saying he has lived in Japan for ten years for the past four years. He enjoys drinking basically anything except straight-up Campari.