I'm going to cut to the chase: I really like Bolt Action. It's simple to play, fairly balanced, and has enough "there" there to be interesting. It's a fun game.
The best way I can describe Bolt Action is to say that it represents a WW2 movie. I'm not a "grognard", and instead I'm far more interested in sociopolitical topics than guns and tanks. I can't tell most tanks apart, don't care about organizational structure, and just don't know or care about a lot of the details people argue about on TMP. I do like Saving Private Ryan and Band of Brothers, though, and playing Bolt Action feels like those. Whether or not those are realistic in any meaningful way is a different conversation, and one I'm not interested in, but the game feels "right" from what I understand World War 2 to be like.
I feel like a lot of this explanation of perspective is important. I like my historical games to be based in history, but to also be based in history that has some distance. I like Vikings because Vikings are quasi-mythological at this point. Sure, it's historical but there's enough distance that jokes and laughs can be had about the setting. Even something like the French and Indian Wars can be talked about and gamed with a certain game-y-ness. These events happened, but they're stories and not pertinent to people today. World War 2 isn't like that, at all, so my reluctance to game that period stems from wanting to give it a certain level of seriousness. But, at the end of the day the game is fun and people actually play it, and there aren't a whole lot of games that have both of those components.
Bolt Action plays fast. The core mechanics play fast, and the game makes a certain amount of sense. I was able to play about 90% of the game using only the 2 page reference sheet after 3 or 4 games.
Turns happen by first each player placing a special d6 into a bag for every unit they have. These dice have 6 different orders you can give a unit, and each turn you take a random die out of the bag and whoever it belongs to assigns it to a unit to carry that order out. You do this until all dice are removed and then repeat. It's fairly basic and shakes up the I-Go-You-Go of many other games, without getting in the way like games with card based activations can sometimes get.
The six orders are: Fire (stand and shoot), Advance (move and shoot), Run (move double), Ambush (Overwatch), Rally (remove pin markers), and Down (do nothing, be harder to hit). Most of these orders are given when the die is drawn, but some (like Down) can be used as a reaction to being shot at and involve taking out an appropriate die and placing that order next to the unit doing that action.
The other big part of the game is that units are given one of three quality ratings: Inexperienced, Regular, and Veteran. This impacts a lot of the game, most importantly their Leadership (which works like Warhammer) and their Toughness value, or target numbered needed to be killed. For instance, a Regular unit will have a Leadership of 9, and will be killed on a 4+. Veterans are 10 and 5+, while Inexperienced are 8 and 3+. These matter a lot as Leadership values receive many penalties, most especially from being "pinned".
Pinning happens when a unit shoots at an enemy unit and scores at least one hit. Each time this happens the target unit receives one pin marker. When that unit tries to do an order it must first pass a Leadership check but with a penalty for each pin marker. A Regular unit, for instance, with 3 pin markers would need to roll a 6 or less on 2 dice to activate. If it succeeds it can remove one pin marker and act as normal, if it fails it instead goes immediately Down.
Vehicles are handled well. So far I find them to be worthwhile without being too good. They're tough to kill, but the game still doesn't require you to build a list designed to kill vehicles. They're generally fairly expensive (with one vehicle being over 650 points, which is a ton in a game designed for 1000 points total) but are fun. Their major advantage is that each gun on a vehicle can fire at a different target, so an IS-2 can (for example) fire its main cannon at a tank, fire its hull mounted medium machine gun at an infantry team in a building, fire its rear facing MMG at another target, and add pin markers to each of these targets should you get at least one hit. Something capable of dishing out that much destruction, and hassle, with a single order die is huge, but it is also a lot of points should it get destroyed by a plucky Anti Tank Rifle Team. They feel balanced, good enough to take but not so good that you have to. There are a few exceptions, I'll talk about those below, but the game works well in incorporating vehicles while still being an infantry game.
That's about 90% of the game. There are rules for things like flamethrowers, mortars, fanatical units, and the like but for the most part the game is very simple and straight forward. As much as I love 40k, and I love it far more than I like it at the moment, I feel that Bolt Action has a lot of that 40k "feel" without having too many special rules and abilities.
Simplicity: The game is fairly simple and straight forward. A Regular guy with a rifle is a Regular guy with a rifle, regardless of what army he comes from. If he's American he can move and shoot without a -1 penalty to hit, and if he's Japanese he has Fanatic, but for the most part there's a certain level of "sameness" across the game that makes keeping up with it simple. Never am I surprised that my opponent's army has a particular special ability and I lose because of it.
Flavor: Despite being simple I feel that the game still has enough flavor to make each nation feel like they should. My Soviets feel like Soviets, my Japanese feel like they are what I think of the Imperial Japanese Army being like. There's enough flavor to keep it interesting without it becoming ridiculous. At the end of the day they're still people with rifles and submachine guns.
People Actually Play It: I would play Warmachine if that was the only game people played. I'm very fortunate that I'm local to Huzzah Hobbies, which has a great group of guys, and that I'm close enough to do Fall-In, Cold Wars, and Historicon which have Bolt Action tournaments.
Relatively Inexpensive: The game doesn't break the bank. Warlord plastics are really solid and it's easy to make an army for under $200. I think my Germans, made of Wargames Factory plastics and Black Tree Design metals, was about $80 from sales they did.
This is still a version 1 of a game. That's a crappy excuse, but there are a few things that don't quite work right that I think can be cleaned up. The game really is 90% of the way there, though, and outside of Saga I can't think of another game that is as fun to play for me right now. Any of these weaknesses need to be viewed in light of Bolt Action being a very good game that is very fun.
Balance: Bolt Action is very well balanced. Germany is clearly the weakest book, but even then it is much closer to the better books than you might think. For comparison, I would say balance between armies is like Power Armor books in 5th Edition 40k. Some are a little better than others, but it isn't that big of a deal. There are no Tyranid or Dark Eldar books in Bolt Action. For what it is worth, I would put Soviets, Japanese, Americans, and British as all being fairly close to one another in terms of power. France and Allies, Italy and Minor Axis, and Germany are all a little bit below that.
When I complain about balance I mostly complain about some of the internal balance in the game. Light Machine Guns aren't very good or really worth taking, for instance, and two five man squads are almost always better than a single ten man squad. Vehicle Flame Throwers are way too good, and too cheap, and that's probably the biggest problem with the game. Even then, most of the rest of the balance issues are fine. I think all the other staples of WW2 such as mortars, snipers, tanks, anti-tank rifles, and the like are all good choices without being too good. They strike the balance of being viable without being so-good-you-have-to-take-them.
Missions: I think this is my biggest problem. I've become very peculiar about missions, and Bolt Actions rub me the wrong way. This could (and should) be its very own post, but right now the missions are my biggest problem. They aren't so bad as to cripple the game, but I think it's the area easiest to fix while also having a huge (and positive) impact on the game. Right now most missions only have one win condition, and as such lend themselves to draws, and force certain builds that make the game feel very game-y. It's not a deal breaker, and a lot of that can be dealt with once you get better at the game, but it is definitely something that I would like to see addressed. But, then again I just got the missions being played at Cold Wars and they are all very good, so I think this is an area that has the most possibility for improvement.
I really like Bolt Action. It has a good feel, plays fast, and just works. There's enough game there to talk about, but not so much that the game is difficult to play. I'm excited to keep painting armies for it and playing it, and expect to play a game or two a week of it for the foreseeable future. Highly recommended.