Oh! I was thinking about this for a while, and couldn't come up with many good games; I can't believe I missed the family of Icehouse games Zarcana, Gnostica, and Zark City.
Zarcana was, I believe, the second game ever designed with Icehouse pieces (or at least one of the very early ones after Icehouse itself). It is played with an Icehouse stash per person and a deck of Tarot cards, with each card having particular powers. At the beginning of the game, 9 cards are laid out in a 3x3 grid. As you play, you try to take control of the cards with your Icehouse pieces; some cards are worth more than others, and you can use the powers of cards you occupy or cards in your hand. Some of the powers, however, involve being able to play more cards, which must be connected to existing cards; or destroy cards, leaving an empty space with a power vacuum. Thus, a changing network of cards emerges, and people develop their own islands or peninsulas of cards to defend from other players.
Zarcana, as an early game design effort, had some problems. The rules were complex and fiddly, without the kind of consistency that allows them to be easily remembered. You had to refer to a rules reference all the time to figure out the power of the cards, or add stickers to help remind you. There wasn't much balance to the game; some cards were so much better than others that if you couldn't start on them you'd be at a significant disadvantage. And games would wind up with each person building out their own little territory, without much interaction from other players.
A group of players and designers (including John Cooper, the designer of Zarcana) decided to fix Zarcana, and redesigned it into Gnostica. The history of how and why they developed Gnostica is a great read for anyone interested in game design.
Gnostica became Zarcana on speed. Gnostica is more aggressive, interactive, strategic, consistent, clean, exciting, and fun. We would never want to go back and play Zarcana anymore. In comparison, Zarcana was too stodgy, tactical, inconsistent, fiddly, random, and difficult.
Gnostica is much more of a gamer's game, with more strategic possibilities, more intense competition, and streamlined rules. Not everyone was a fan of the redesign, however. Andy Looney, of Looney Labs fame, happens to like games that are somewhat more random, chaotic, and quirky, with quicker turns and lighter gameplay (as you might guess from his most popular game, Fluxx). He wrote a great essay on why he prefers Zarcana, which is worth a read to help figure out which game you will prefer.
Finally, to promote the 3HOUSE bundle, Andy Looney developed a game that uses similar mechanics of controlling cards on a changing grid called Zark City. Zark City is a classic Andy Looney design; simpler, quicker playing, and more accessible than Zarcana or Gnostica, with a larger amount of luck. It uses ordinary playing cards, instead of Tarot cards, which also helps make it more accessible.
The Zarcana family of three games, all related and all using Icehouse pieces, involve a connected network of cards with different powers, which change throughout the game, and which players control.