It seems that the most popular card game is Whist - not classic Whist but a version with two phases of bidding, the aim being to win the exact number of tricks that you bid.
Yaniv is a draw and discard game that has recently become popular.
The tile game Rummikub® was first promoted in Israel, where it was apparently very successful. As far as I know it has remained popular there.
The World Casino Directory includes a listing of Casinos in Israel.