Samsung Galaxy Note comes with a pretty massive battery and reports of battery runtimes have been quiet positive. However, if you are heavy user or you play a lot of games, you might want to invest in a second battery or a bigger battery. Seido makes a 5000mAh extended battery called Innocell for the Note. This is double the capacity of stock battery. Here is the review of it.
Seido battery weighs 99gm (stock weighs 49gm), so yes it does adds a lot of bulk and thickness. However, it you get lot of runtime. Earlier, I was getting around 8 hours and now, this monstrous battery yields around 17 hours.
A normal user will get almost 3-4 days with average use.