I recently invested in a Decktet, which is an interesting alternative deck of cards. It has 36 cards in the default deck, in six suits of ten cards each - which is accomplished by way of the regular rank cards having two suits each. As can be seen in the above image, each card also has a name and an illustration in a similar manner to a tarot deck; there is in fact an interpretation guide on the website for people so inclined. Additionally, each card (apart from the aces [ones] and crowns [often but not always tens]) is categorised as either a 'personality', 'location' or 'event' (or sometimes more than one). There's an extended Decktet, which includes pawns and courts (each with three suits) and a single wildcard, the illustration for which contains elements from each of the six suits.
What does all this mean? Well, quite a different approach to constructing games than that seen with a regular 'French' deck of cards. For example, one kind of French-deck game I enjoy is the Rummy family of games. In Rummy games, cards are collected into 'melds' made from groups of cards sharing common characteristics; either cards with the same rank, or suit, or in a run of cards. Throughout the game, you'll be constantly exchanging cards, trying to build good-scoring melds in your hands as you discard the cards you don't want and hope to draw better ones. Cards you discard are available to your opponents to take instead of a draw, so if you suspect they're collecting hearts, you might keep the eight of hearts in your hand even though you have no use for it whatsoever.
In a Decktet game, your eight won't just be one suit - it might be the eight of wyrms and knots, as seen above. So not only do you have to be doubly careful when you throw out a card, because your opponent may be collecting wyrms or knots, but also there's more chance you might want to use it yourself. A Decktet Rummy-esque game might even not demand that each card in a meld shares a suit, but that each card shares a suit with the next card over in the meld - meaning you could chain the eight of wyrms and knots with a knots and moons card and a moons and leaves card in the same meld.
Is this better? No, but it's not worse either, and it's interesting in its novelty. One of the 'example' Decktet games on their website - Adaman, a solitaire card-matching game - makes exemplary use of the deck's unique structure; the goal of the game is to 'capture' all of the personality cards by playing rank cards of similar suits with at least the same value. You quickly find after a couple of games that the suns and moons are your critical suits, necessary for capturing the most powerful of the personalities, so you need to be careful how and when you spend them; you may have a 5 of moons and leaves which you could use for a few leaves to take out a lower-rank personality, but it's probably better to keep the moons for later. In fact, you'll often end up capturing other non-personality cards just to get a better range of suits; switching The End (crown/ten of leaves) for The Forest (five of moons and leaves) loses you five rank, but maybe you don't need the leaves at all and you're really short of moons, and it's worth it. The deck seems to have been constructed fairly carefully to have certain pairs of suits which are frequently together, and other pairs which are uncommon or entirely left out of the regular deck.
I'd thoroughly recommend that anyone interested in card games at least give the Decktet a try, anyway. There are a number of pretty good games to play with it (and of course, some pretty crappy ones), and - well, it's something new and interesting. The downside is that it's not so easy to get hold of a copy. You can print out your own copy [PDF]; if you're in the US you can buy a deck from TheGameCrafter.com, a print-on-demand cards-and-pieces supplier; everyone else can order from ArtsCow, which some people have found to be a bit hit-and-miss.