NTFS is a more secure and sophisticated file system than FAT32. Chances are though that if you don't already know which NTFS features you need (meta-data, indexing etc.), then it's not something you need to worry about converting your file system too. FAT32, according to some techies, is a bit faster than NTFS because it is less complex.
In my experience, I've found that greatest stability gain with your file system doesn't matter so much on which type of partition you use, but rather on the stability of the operating system itself. NTFS partitions are more stable than many FAT32 installations out there because NTFS is always used in conjunction with Win 2000 or WinXP. Using FAT32 with these modern OS's (instead of with the erratic likes of Win ME and Win 98) should be just as stable for the average user.
Remember though, that if you do convert to NTFS, there's no going back to FAT32 without having to buy a third-party partition program like Partition Magic.
Plus, like Amoraq314 said, try to avoid NTFS if you're going to be using Linux. Reading NTFS partitions from Linux is easy, but seamlessly writing to an NTFS partition is still not well supported.