Mexico is thought to have been the place of origin of the first western rummy game Conquian, which spread from there to the USA around 1860. Conquian is still played in Mexico, using a 40 card Spanish cards pack, lacking 8s, 9s and 10s. There are versions for two and three players.
Pokar is a Draw Poker-like game with the 40 card Spanish pack. Only four cards are dealt to each player, and the only valid combinations are four of a kind, three of a kind, two pairs and one pair (apparently there are no flushes or straights). Players can discard up to 3 cards and draw replacements. The ace of coins is a wild card.
Burro Castigado is a children's game, related to Pokar. Each player is dealt 5 cards and can discard up to 3 and draw replacements. Valid combinations are four of a kind, two pairs, three of a kind, one pair; the highest hand wins. There are no wild cards.
In Siete Loco the aim is to get a score as close to 7 as possible without exceeding 7. It is played with the 40 card Spanish suited pack. Pictures are worth half a point and numeral cards are face value. Each player is dealt one card initially and can ask for additional cards. There is a variation in which the aim is to get seven and a half points.
Malilla is a version of the Spanish game (there called Malilla or Manilla), played with the Spanish 40-card pack.
La Viuda (the widow) is the Mexican equivalent of the American game Whisky Poker.
I would be grateful for further information about these and other Mexican card games.
The World Casino Directory includes a listing of Casinos in Mexico.