The Non-Euclidian Staircase

Battle Line is our Knizia game for this entry. This one is a two-player card game that nominally simulates battle between Alexander the Great and the Persian King Darius. But this thematic bit is not really important, as you don't even determine which player is which historical figure until during play, and may never know if the two leader cards don't come into play; as with many Knizia games, the theme is mostly an excuse to hang an abstract mathematical game from. This time, the game is a progressive effort to build up 3-card sets at each of nine "battle flags", where each card represents one of 10 different troop types (numbered 1 to 10, named and illustrated in ascending order from lightly armed skirmishers to massive battle elephants) . Sets made up of the same troop type, troops of the same color, or troops of types that form a sequence are superior to random sets (you could think of them as 3-card poker hands, if you like), so players carefully decide where to place their strengths to form the best formations. You play only one card a turn, and all cards are played face-up, so both players know everything about the game except what is in the other player's hand... and their devious little mind. Victory is achieved when you win either 5 battle flags (the majority) or 3 adjoining battle flags (a breakthrough). Each flag is decided when it becomes obvious that your set overpowers the opposing set. Note that this can become obvious even if one or both sets is incomplete! If, by counting face-up cards, you can demonstrate that no card still unplayed would result in the weaker set winning out, the stronger side takes the flag immediately. This rule results in some odd strategies, such as trying to lure your opponent into playing a second card toward a set you know (because the card they need is in your hand) they'll never be able to complete, or playing a card to show it isn't available, thus demonstrating a set at a completely different flag to be a loser. That latter strategy can result in you taking two (or, rarely, three or more) flags with one play! There are also "tactics" cards that keep the game from being too predictable, because they do things like modify the set rules for a single flag or cause a card to change sides. This is a very fun game of abstract strategy, with enough depth to require thought, but with sufficiently limited options each turn to avoid the game bogging down into unending quandaries about what to do next. Play is quick (20-30 minutes), so you can even go for a "best two out of three" play to minimize the impact of luck.

Munchkin is a light, silly game mocking dungeon crawl RPGs. Player take the "roles" of various dungeon invaders though you can change exactly roles pretty much at any time if, say, you get bored with being an elf (something that usually happens right when a monster that specializes in eating elves shows up). Play consists of tossing out cards to fight, then gathering up treasures and experience when you win (or taking damage when you lose). Other players can toss in cards to help or (more commonly, unless you bribe them) harm your odds against the monster you find. The object of the game is to be the first character to make it to Level 10 thanks to your monster-killing prowess. Expansion sets (2 so far) add even more silly roles, monsters, magic items, et al, to the mix, which just increase the silliness. This is a fun game to just sit around and read the cards (and enjoy the John Kovalic art)! But unlike many games that are just fun to look at, this one is also fun to play, preferably with as many people as you can gather to increase the madness (and the likelihood there will be at least one player currently in the role that your nastiest cards target!). Space Munchkin takes the same game into SciFi with minimal changes (in fact, the games can be somewhat intermixed if you like), and there's also Munchkin Fu that promises Martial Arts smackdown silliness (I will admit that I haven't actually seen it yet). And, on the even sillier side, there are three familarly-titled volumes that translate the cards of Munchkin to d20 rules (with allowances for a drastically increased power curve), in case you like your dungeon crawling this silly.

And yes, this was on the list to be included before Jenn's comment, though it's nice to know I'm not alone liking this one (though, with Munchkin, I would have felt pretty safe assuming that).

And here's an additional note... Many of the games listed here and in previous entries are available for purchase at Funagain Games. Here's a convenient set of links for the available games mentioned so far (and yes, these are "associate" links that gives me a little bit back on any referred sales... do support your friendly local game store first, but if they can't get the title, do give the folk at Funagain a try!). Future "Favorite Games" entries will include these links as well, at least as long as the games are available (sadly, not all the games I have already listed are, and I'm sure some future faves won't be, either).

Funagain Purchase Links:
Settlers of Catan
5-6 Player Expansion
Seafarers of Catan
Seafarers 5-6 Player Expansion
Cities and Knights
Cities and Knights 5-6 Player Expansion

Ursuppe
Ursuppe Freshly Spiced Expansion

Kill Doctor Lucky (director's cut)

Lord of the Rings
LotR: Friends and Foes Expansion
LotR: Sauron Expansion

Lord of the Fries (special edition)

Munchkin
Munchkin II - Unnatural Axe
Space Munchkin