I have a GF4ti4200 64mb video card. What i want to know is with mine and
other newer video cards does the size of the video memory from 64mb, 128mb
and 256mb matter that much for todays games?

It matters to some extent. With Unreal 2 for example, you do not want to
play with the texture slider whacked up all the way to the top, that will
cause severe drops in framerate since all textures for a level can't fit in
on-board memory. A 128MB board will help here. Some other high-profile
titles may behave in a similar fashion.

Also, high resolutions with high antialiasing settings use an incredible
amount of memory, 1600*1200 at 6x antialias uses a total of 100+ MB of
memory just for screen buffers alone, which means you pretty much HAVE to
have 256MB to use such resolutions. Of course, the fillrate on current cards
(even high-end ones) isn't high enough to run games efficiently at this kind
of resolution, so it matters little anyway. Was just making an example.