I have about 4-5. I have 2-3 brown ones, 1 purple, and 1 blue. These palettes have about 4 shades of the color in it. I think I'd like to have a green palette eventually, and maybe a grey and black one for smokey eyes-- even though one of my brown palettes is a smokey eye. I don't really have a need for tons of palettes. Just enough to switch it up once in awhile, and enough to cover the basic colors. Most of my eye palettes are Maybelline (I love them)... I have a Victoria's Secret palette and a Rimmel palette. Don't care for the Rimmel very much, but VS is great (it's my everyday, brown one).
On a related note, I HIGHLY recommend a eye shimmer primer of some sort. I get mine from Victoria's Secret-- it's called Eye FX. One is brownish for dark colors (like brown, black, or sage) and the other is silver for bright colors (like blue or purple). It makes your eye shadow so much more bright and concentrated looking.