Ascension1 is one of the more popular deck-building games around today -- probably the most popular. It was first published in 2010 and has passed the point of being new and exciting, but the publishers have come out with a number of new editions (eight, by my count, not counting special anniversary editions), and have released an app that allows you to play against an AI for free or your friends if you buy the full version for $1.99, all of which has kept the game in circulation in the face of an healthy market of copycat games.2
Deck-building games have a simple and addicting mechanic. You start with a small deck of crappy cards -- in Ascension it's ten cards, eight 'money' cards and two 'fighting' cards -- and use these to gain better cards. Some of the cards you earn will allow you to remove the less desirable cards from your deck. Each turn you draw five cards from your deck, play them as you see fit, and discard them. Once you have gone through your deck, you reshuffle your discard pile and start again. By the end of the game you have built yourself a deck optimized for your chosen strategy, but so have your opponents. You all count up your points and see how you did.
Ascension is a fantasy-themed game, with factions in the base deck approximating nature spirits (Lifebound), warriors (Void), mystics (Enlightened), and steampunk (Mechana). The art is quite nice, but it is not required that you care one whit for fantasy to enjoy this game.
All players have access to a row of cards up for purchase or battle. These cards range in price from 1-8 cost, or 3-7 damage for the monsters. There are also 'cheap' cards, which can always be purchased and never run out. Your start deck contains exclusively cards with either a purchase power of 1 or a damage value of 1. The cheap cards will gain you a purchase power of 2, a damage value of 2, or an easy monster (a cultist) to conquer for just two damage. While these give you easy ways to improve your deck, you are really aiming for the special cards -- a set of five cards that are replaced upon purchase. These all have different abilities -- gain one victory point, draw an extra two cards, remove ('banish') an undesirable card from your discard pile, 3 damage to a monster, acquire a card from the center row for free, etc.
Some of these cards are 'constructs' -- cards that are not discarded after you play them, but stick around to give permanent benefits. At least, permanent until another player manages to destroy them.
And finally, what you are ultimately playing for is not purchasing power or damage, but victory points ('honor'). These are gained both by defeating monsters and for the cards that you collect in your deck. As you might guess, the player with the most victory points at the end wins.
Ascension is designed for 2-4 players, and will take about 30 minutes to play, depending on number of players and how familiar they are with the game. It is usually recommended for ages 13 and up, although I suspect that most players are in their early to mid 20s.
As I've said, I quite like this game. It is currently my favorite deck-builder game, and it is widely available and well-known. It also has plenty of expansions and alternate decks. I would recommend this game to anyone who likes the new wave of board games (Settlers of Catan, Pandemic, etc.). Not only is it a fun game, it is also easy to learn and fairly cheap (about $10-15 for the two-player 'Apprentice Edition' base game), making it a good introduction to deck-builders.
The current expansions are:
1. Ascension was originally released as 'Ascension: Chronicle of the Godslayer', and the original base game is sometimes still referred to as such, usually in the initialization CotG.
2. It is worth noting that the game that popularized the deck-building mechanic was not Ascension but the 2008 game Dominion. Copycatting is fair game in the gaming industry.
Board Game Geek is an excellent site to read more about this, and other, games.