The key word is "generally". Zinfandel is very much associated with the style developed by Rosenblum, Ravenswood, and the -elli's in California: huge black fruit profiles, huge alcohol, flashy, forward, spicy, rich, almost port-like, with lots and lots of primary flavours but lacking acidity and aging potential. Of course this is not true for all Zins, but it's a general overview of the California style.
Of course, not all Zins are made this way. Try a blend from Ridge -- Three Valleys as an introduction, or Geyserville if you have some extra cash burning a hole in your pocket. It's a much "cooler" take on Zin, less intense and in-your-face, and the blend adds some interesting smoky and meaty complexity.
On the other stylistic side, try some Primitivo from Italy. It's a Zinfandel clone (or, more properly, Zin is a Primitivo clone) with a completely different flavour profile. Earth tones, acidity, and a flavour profile leaning more towards red fruit is more the speed with this grape.