By ship
The overnight boat service between Hangzhou and Suzhou/Wuxi has been discontinued. You can still take a ferry along the Hangzhou-Beijing Grand Canal to the north of Hangzhou proper see "water taxi" section below.
By train
There are frequent high-speed trains connecting Hangzhou and Shanghai. The CRH train train numbers starting with G from Hangzhou to Shanghai's Hongqiao Station is 50 minutes non-stop ¥78. Some services have intermediate stops and take 55-60min. The trains have recently been limited to 300 km/h for safety reasons.
In addition to Shanghai, Hangzhou Train Station serves trains from Guangzhou, Beijing, Chengdu, and everywhere in between. For destinations further away, such as Kunming and Urumqi, you would first want to go to Shanghai or some halfway-point train station. There is an East Train Station as well, but it is not in such a smart part of town. Trains returning from Shanghai often only stop here rather than at the main station.