I just noticed that cats seem to have very close eyes to certain reptiles (mostly snakes and lizards).

 

Were felines and reptiles much close biologically in the past?

Felines were no closer to reptiles than other mammals, and belong on the branch that split from the reptile line a little over 300 million years ago. While some reptilian eyes are very similar to a cat's eyes, I would think the similarity is mostly visual, and the underlying structures are quite different.

 

http://en.wikivet.net/Lizard_Eye

http://www.earthlife.net/mammals/vision.html

Just to add to pwagen's response, you may want to look up homologous vs. analogous traits.