A game that I've been eager to play for quite some time was 1960: The Making of the President.
In 1960, one player takes on the role of Richard Nixon and the other player is John F. Kennedy, and they are both attempting to win the 1960 presidential election. The game is played over 9 turns. In 7 of the 9 turns, the bulk of the turn consists of playing 5 cards. The cards can be used either to activate their event or for their "CP" value. If you use the CP on the card, you can do one of the following 3 things: campaign (and each CP translates into influence in a state, or allows the candidate to move), position yourself for issues, or mount an advertising campaign. Each time that a card is used for CP, your opponent has the opportunity (if they have enough momentum) to activate the event that is in the text of the card (unless you preempt them using your momentum). The final card(s) each turn are placed in your "campaign strategy" pile. The 6th and 9th turns work differently. These turns represent the Debates and Election Day. During the Debates, the candidates use the cards that they previously had placed in their "campaign strategy" in order to try to win the debates (to get more state influence). During Election Day, the players get to perform a few last support checks to try to get extra influence, and then they add up their total number of Electoral Votes to determine the winner.
The first thing that I really enjoyed about 1960 was how "support checks" worked. Various things (like campaigning where your opponent was located) require support checks. There is an opaque bag which is originally seeded with 10 cubes of each color. Each turn, as players play cards, they gain "rest" cubes (the lower the card's CP value, the more rest they gain). At the end of each round, these rest cubes are added to the bag. Any time that a support check is required, cubes are pulled from the bag and if you pull your own colored cubes, the support check is successful. This was a really interesting mechanic, and was also nice to help balance cards that are weaker in the game - if the card is less helpful immediately, it will be more helpful long term.
The next aspect that I liked about the game was Momentum. There were a couple of ways of getting momentum: either through successfully positioning yourself on issues (you would gain momentum at the end of the round), or by playing events that gained momentum. Here's what Momentum was used for: one momentum triggered an opponent's event when they played a card for it's CP value; two momentum preempted an event to prevent your opponent from triggering it. The actual triggering of events may not actually occur all that often in a game (because you are typically trying to avoid allowing your opponent to activate your events), but it definitely plays a major role. Instead of being able to play the cards that help your opponent without any penalty, now you must be very careful of the order that you play cards and how much momentum your opponent has while playing them. This may have been my favorite aspect of this game.
A third pro that I found while playing 1960 was the importance that all of the different options had in the game. If each player plays all of their cards for campaigning (gaining cubes in states), then the game would be quite boring. However, because of things like momentum, it is important that you use some cards to position yourself on issues, some to campaign, some as events, save some for debates or election day, and use some to advertise. Any of the elements of the game that you ignore can significantly be used against you. As an example, if you don't position yourself on issues, then I will gain extra momentum (letting me trigger events on your cards) and gain endorsements (allowing me to win in states which neither player has influence over). Another example, if you fail to campaign, I will simply defeat you by having more influence.
My final pro for the game is true for each of the games from these designers (they also designed Twilight Struggle and Founding Fathers if my information is correct) - the historical depth of the game is amazing. I am by no means a historian, but here is something that I now know because of the game: Eisenhower was horrible for Nixon's campaign. Every time that I drew a card with Eisenhower's picture on it when I was playing as Nixon, I knew the card was going to be horribly negative for me. The pictures and the flavor text for the cards help me learn history while playing games - sweet!
The neutral thing for me to mention is the tug-of-war aspect of the game. This is neither a pro nor a con, but definitely something you should be aware of going into the game. Since the game is based on winning favor of the different states back and forth, there is definitely a tug-of-war feel. You may be going back and forth with a single state most of the game (New York), and thus you're really frustrated if you lose that state - even if you win the election!
Now for the cons. The first con is that I felt like "controlling" a state did not matter enough. You "lead" a state if you have influence in that state, but you "control" the state if you have four or more influence in it. Controlling a state forces your opponents to perform "support checks" when trying to add influence to that state. However, with the sheer number of events that add state influence directly (with no support checks needed), there are far too many ways to break an opponent's control without having to perform this check - and so it winds up being fairly pointless to spend enough influence to actually control a state. This really frustrated me about this game, and was the single biggest factor for which I dropped it's score. I also think that this limited the replayability of the game to an extent.
The next con to the game is more of a "missed possiblity" than a true con. The candidates in the game are too similar. I realize that this was setup to balance the game, but it would have been nice for the candidates to have more personality. Whereas in the game as it is now, it does not matter too much which candidate you play, I would have liked for it to matter much more. I would have liked Nixon and Kennedy to have different strategies, strengths and weaknesses, or something like that. There are different cards that set them apart, but most of the cards balance out, as do starting positions, and everything else in the game.
Overall, I give 1960 a 9.0/10. I debated this back and forth, and I definitely don't like it quite as much as Twilight Struggle. But, I do really like the game, and if you enjoy games where you're constantly struggling back and forth with your opponent, this is something you should try.
If 1960 sounds interesting, you might also check out Campaign Manager 2008, Glory to Rome, and Mage Wars.