Fluxx

Fluxx is a non-collectible card game with some fun (and unique) gameplay mechanics.

The basic rules are very simple- on your turn you draw 1 card and play 1 card, and the first person to meet the Goal in play wins. But the gameplay itself is a bit more unpredictable than that, due to a variety of card types and effects.

Cards in the game are split into;

New Rules - Change how the game is played, even during your turn when you can break the rules in play (to an extent) so if the rule Hand Limit 0 is in play, you can still hold cards until it isn't your turn any more. Rules generally make the game more frantic (Draw 2,3,4 or 5) or less predictable (Play 2,3,4 or All) or make other players groan in frustration (Hand limit 0,1 or 2.)
Actions - Do what they say on the card. Most of these make people groan as you do things.
Goals - Are how you win the game. At the start of the game, there is no goal, nobody can win the game until a goal is played. Generally involve keepers, but some require creepers, or even a certain number of cards in the hand.
Keepers - You get to keep, and are played in front of you. Many of the goals involve at least 2 keepers.
Creepers - Like Keepers, but they have to be played straight away, and usually stop you from winning if you have any. However, some goals actually require Creepers to win.
Surprises - Forthcoming with Pirate Fluxx, these cards can be played on an opponents turn to negate their card.

Fluxx (and its variants/expansions; Family Fluxx, Zombie Fluxx, Eco Fluxx, Monty Python Fluxx, Stoner Fluxx, Martian Fluxx, Pirate Fluxx, Star Fluxx, Oz Fluxx and Cthulhu Fluxx) all come from the very excellent people at Looney Labs

Tropes used in Fluxx include:

Anti-Magic: Surprises
Discard and Draw
Extra Turn: The Take Another Turn card.
Gameplay Roulette: Nearly half the cards in a given Fluxx deck have this effect.
Incredibly Lame Pun: The majority of the Goal cards
Level Editor: Fluxx Blanxx allow you to make your own cards.
Shout-Out: Several of the cards mix this with the above (including All You Need Is Love and Death and Taxes)
Xanatos Speed Chess: The only way to play with anything approaching strategy, since the rules and victory condition are always changing.