I am installing Gentoo onto my computer and I was wondering if I need to have swap space. I have 512 megs of ram, definitely more than enough for what I am using this computer for, do I even need to have a swap partition? If so can it be 32 mb? I have heard that no form of linux uses over 128 megs of ram per partition of swap space, so I was wondering what the bare minimum needs to be for linux to successfully install and run. Is Swap detrimental to linux kernel compiling and booting successfully?

You don't need a swap partition. A swap partition is handy if you don't have that much ram. I believe i had problems compiling kde with only 256MB of ram. Otherwise it's a complete waste of a partition.
IF you later decide for some reason that you need it, you can create a swap file on your file system that functions the same way - hence no need to pollute your drive or your partition table.

to create a swap file:
dd if=/dev/zero of=/mnt/swap bs=1k count=65536 (example 64MB swap file)
mkswap /mnt/swap
swapon /mnt/swap

you will need to place an entry in fstab for the swap to mounted at boot time. Or you can place it in a script if you like.

This is a better solution for when you really need it. I solved my kde compile by just creating a 64MB swap file and then removing it once i was done.

You don't really need one.
I have a GB and I've only once come close/exceeded it
and if you all of a sudden need swap space
(b/c your friend brought over an unbelievably large picture
of the earth from space)

...nm my friend xexix got it