Oh me, oh my. Where to start?
Not really "obscure", but DIPLOMACY gets my vote for best game, ever. It's an amazing party game, and I try to make it a point to play at least once a year. A few years back, I even employed my brother as a spy (he wasn't playing the game) - he would sneak around and eavesdrop on other players' conversations, and give me a report later on. I was playing Austria at the time, and this was how I found out that my ally Turkey had decided to betray me and switch over to Russia's side. The info was enough to get Italy in on my side (we were neutral; Italy and Germany were working together to take out France, but Italy wasn't really get much out of the deal) and pre-empt against Turkey.
The game is absolutely a must for every gamer. There are seven players, and everyone writes down their moves before every turn. No dice are rolled; the game is resolved by deciding which armies support what and which armies move where. Since there is a lot of room for "Complications" (ie, two armies trying to move into the same territory... a problem, since only one army is allowed in any territory), you had to work closely with your allies.
The great thing was that you had a party atmosphere where you would plan moves and discuss strategy with every player at the game. And it's anything goes - the only "rules" of the game occur after your orders are resolved. So, if you want to lie, cheat, steal, bribe, whine, or whatever else, feel free. It's an amazing game, and almsot a role-playing experience.
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I also like Flying Buffalo's Lost Worlds series - you buy a book that depicts a character, and you use this book to duel other players. It's a dueling system that works very well,and you can even (sort of) use it to stage multiple combats at once. My personal favourite character to use was a warrior woman with a shield; later, they added monster books (dragon, skeleton, troll, and the like) that were a lot of fun to play. You could almost turn the game into a single-player RPG, which is something we did a few times. Fun stuff, and great for when your game night fizzles.
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BATTLETROOPS, by FASA, has got to be one of my all-time favourite games. It's set in the BATTLETECH universe, although mechs aren't the major focus of the game. Players run small-scale foot squads in an urban environment. The game comes with several building floorplans that work as tactical maps; players create and equip their squads, and run out various scenarios provided in the scenario booklet.
The game is great because of the use of time units to measure what a character could do. The more you moved, the fewer points you could spend to set up firing arcs (the less you spent, the smaller your firing arc was, meaning your character would have to carefully "aim" his shots). If you crossed into another character's firing arc, the player had the opportunity to interrupt gameplay and take a shot at you.
We had a lot of fun with this; I remember running various scenarios where my Steiner-Davion commandoes (I had a group of eight men, who all had varying equipment and had even been named) against an Evil, nasty group of Kurita Scum (who had been selected simply because their tokens "looked the coolest").
Our squads weren't very tactical, simply because it was just much cooler to bust open windows, toss grenades around corners, and generally cause a ruckus.
I wish I could dig up a copy of that game. It was a blast.