I believe 32 is the maximum number of textures that can be bound currently. As far as I can tell even the 8800 series had 32 texture units.
As far as I know, for openGL 4.x support you will need a Fermi or newer nvidia card(or corresponding amd card), the higher end models all seem to have 32 units, while the lowest end cards (GT 430, for example) have 16.
However, looking at AMD spec sheets they list numbers like 80 or 128 texture units, but list 32 color ROP units which seem to have remained constant through generations.
The GTX 480 on the other hand is listed with 60 texture units and 48 ROP units, while lower end cards like the 430 reportedly only have 16 texture units and 4 ROP inits.
So on the whole I'm not really convinced either of those is the number you are actually looking for.
You can check the number of texture units available for non-fixed function pipeline rendering with
glGetIntegerv(GL_MAX_TEXTURE_IMAGE_UNITS, &texture_units);, though, so if you have access to some diverse hardware you could check yourself.
EDIT: this site lets you compare the reported openGL capabilities of all sorts of video cards, that should give you the numbers you need: http://feedback.wildfiregames.com/report/opengl/device/GeForce%20GTX%20580
PS: AMD and nvidia have recently introduced "bindless textures", (amd has a different name for it) which allows you to use large numbers of textures without binding them to textutre units, at the moment this is only available in openGL.