Unfortunately not! You have to be very careful not to miss the last train, which is usually around midnight. Google Maps has a really good transit planner and will show you last available transit options for the night.
Some outer city trains will run later to allow connections from central Tokyo, but when you go for a night on the tiles in Roppongi for example, a decision has to be made! If you're lucky to live close to a nightlife area, you can walk or splurge on a cab (they're expensive here). If not, stay at the bar or club of your choice (a lot are open very late) and take the 5am train back with the sunrise! I do wish there was a night bus like London or some occasional train routes past midnight.