I have a tile counter top, white, I need to know what materials can be laid over the tiles? Laminate? Quartz?
Or should I just pull the counter tops and redo tile?

Pull it up and redo or just get totally new countertop material. Nothing will go on top of the tile without looking like crap and not lasting very long.

Take a look at the new countertops Home Depot is carrying.
There Formica but there a totaly differant profile and look very much like a real stone top.
Took me far less time to install then it would have take to tile them and I ended up with nice easy to clean tops.