How many hours of shooting do you usually do before your battery dies?

I know that this varies for different cameras and also depends how much power your battery is capable of, but I just wanted to know. I will be on a sight-seeing tour for about half a day and I'm debating whether or not I should order a spare battery for my camera. My camera is a Nikon D5100 with a 1030mAh lithium-ion rechargeable battery. I haven't really used this camera for a long period of time so I'm not sure how long the battery lasts.

You've answered your own question with your first line… It depends…

I shoot a Canon and I can get about 30 to 45 minutes of video on one battery.

DSLR camera batteries generally have an excellent life and I'd doubt if you would need an extra battery. If you'd looked in your camera Manual (Specifications, Page 236. You would have found the approx.battery life (which also depends on the temp. And how the camera is used… Read the specs page).
You'll get approx. 600 shots, single-frame release mode, continuous release mode approx. 2200 shots.