It depends on what you are running, and having 8 tabs open in your browser is NO multitasking.
Some games, some video encoding apps, some rendering apps will make use of more than one core. They will spread the load among multiple cores so the work gets done faster. Some apps will use only one core no matter how many you have open. Toms has done tests with some games to see how many cores would make a difference, and they discovered that a lot of common game see a speedup with 3 cores, but then going from 3 to 4 doesn't gain much.
Now something that I notice with my own computers- if I have things running such as a virus scan, background plotting, copying files, downloading files, I can continue to operate whatever else I am interacting with and not see a slowdown when using my machine with a quad core. But when doing this on my machine that has a dual core at 3.8GHz, I can see a slowdown.