FAT32 - Old filesystem. Unless you really want Windows and Linux on the same partition, there's no point in installing to this filesystem. It has a variety of problems and it's probably safe to say Microsoft kept it in use for much longer than they should have.
NTFS - You are correct, Linux cannot be installed to this, as writing to it from Linux is considered dangerous. I've heard there are tools for doing it relatively safely these days, though. At least it's an improvement over FAT32.
ext2 - Another old filesystem, but it's not bad. You have to be careful with it. I remember a while back having to cut power to my machine because Mandrake hard locked on me. I tried to reboot and found that the filesystem was corrupted, so I reformatted. Thinking back on it, it was probably fixable, but I didn't know anything about that at the time.
ext3 - This is a journalized version of ext2. Basically, it's more forgiving than ext2. You also don't have to fsck it every time the system goes down hard. A good thing about ext3 is that if you're running an ext2 filesystem, you can add the journal to it, basically converting it to ext3, without losing data. One catch of using a journaling filesystem is that the journal takes up some space, making it unsuitable for small partitions(in the area of tens of megabytes), like a boot partition, or floppy disks. To minimize risk, people with a seperate boot partition typically make it umount as soon as the system is up and running.
ReiserFS - This is another journaling filesystem. It's younger than ext2 and I think ext3 as well, but it caught on quick. Many desktop users run this filesystem, myself included.
http://www.namesys.com/
Here's a Linux Magazine artical about ext3 and journaling filesystems. It's on page 3, which talks about journaling filesystem, just go back to page one if you want to read the whole thing.
http://www.linux-mag.com/2000-08/journaling_03.html