On Windows, DF by default can need up to 2 GB of memory (RAM), depending on the size of your embark horizontally (e.g. 5x5), the vertical size (layers of sky, of dirt and stone, the stranger stuff beneath, etc. can vary quite a lot depending on randomness and what you set for your world gen parameters), and things like the length of your history (which adds more records of battles, more historical people and locations to keep track of, etc.). Unfortunately if it for whatever reason tries to exceed either the 2 GB limit or the actual remaining available memory on your PC, it is highly likely to crash.
If your computer has more than 2 GB of memory (RAM) that is working properly, you should be able to go larger than 5x5 under at least some conditions. Note that DF uses memory much more aggressively, and is somewhat less fault tolerant, than many other ordinary user programs; if you think you have plenty of memory you might want to check it with something like
Memtest86+ to make sure you don't have a bad chip. Note also that some overclocking is not long-term stable enough for DF, even if other programs can manage to run.
If you have at least 4 GB of tested, stable RAM you may want to look at patches for making DF "Large Address Aware". This is a somewhat peculiar Windows thing that should allow DF to use up to 3 GB instead of 2 GB, at the possible cost of some stability and/or compatibility.
There are a variety of other posts about how to tune the world generator to have flatter, or more boring, or otherwise lower-memory embarks; it's all about tradeoffs. Unless and until Toady takes the (possibly enormous) amount of time to make DF 64-bit aware (which, to be clear, is not even on the horizon in any official way), players will need to make choices about what their limited memory gets "spent" on; horizontal size, vertical size, civilization complexity, etc.