Although a lot of people have answered the OP, I've got some experience with some of these and I thought I'd put in my two cents. Plus, I'm trying to avoid studying, so this might go on a bit.
Arkham Horror:
One of the first co-op games I bought. I liked it a lot initially, but it doesn't get played much anymore. The base game is great all by itself, at least until you've played enough times to understand some of the mechanisms under the hood - Once you know those, it takes you out of the theme and reverts you to playing odds a bit. The first game you play will take a *long* time, both to set up (lots and lots of different card decks and tokens, etc) and to play. The reason is mainly learning the order of operations for a turn, and making sure you do things correctly. The manual (like almost all fantasy flight games) is pretty terrible for this - it's not well thought out and finding the information you need always takes longer than it should. The single best advice I could give is to find a Summarised rule sheet on the web that fits all the important stuff on to one page, and print a copy for every player. Once everyone knows where to look on that sheet, they've got everything they need to know. The only caveat: if the sheet mentions the frequency of certain cards or locations, cut that part out (part of knowing the underlying mechanics ruining the fun). I've played a couple games with the Innsmouth Horror expansion - the single best part is that it makes all the decks of cards bigger, so you're less likely to see repeats.
Space Alert:
Great game. Hugely fun. First time learning takes a while, but you're playing games as you go. If everyone is enthusiastic about listening to you read the tutorial and learning one step at a time, you'll have fun, even in the tutorial missions. If you get some new people in and throw them in the deep end, they might have trouble, but it's still fun. I've only ever played with the full complement of 5 - it's supposed to work with 4 (a more common number for my group), but 5 is so glorious that I don't want to sully it. One word of warning - if you try to introduce this to family, make sure before you start that everyone is a) paying attention and b) at least a little intelligent and c) going to understand the concept of "programming" your guy, rather than playing him directly. I ruined last Christmas by not heeding these rules.
Pandemic:
Great the first couple times, dry after that. After a couple of games, it's easy to work out what the optimum course of action is in any situation. Once you know this, the easiest difficulty is a joke, medium difficulty is ok but not exciting, and hard difficulty is boring because whether you win or lose is dependent entirely on the shuffle of the cards, and almost nothing the players do can change that - even playing optimally, the win rate on hardest difficulty might be 10%. Once you lose 5 of those in a row, all desire to play the game evaporates. It's probably a good entry game for someone who isn't that into board games, but I wouldn't recommend it to anyone else.
Descent:
A One-vs-All game. The guys at Shut Up and Sit Down like this a lot, but I've never really gotten into it - some of my group like it, so we play it every so often, but it's never sat right with me. The second edition is better than the first, and more fun, but I still find it more frustrating than rewarding. The missions aren't particularly well designed - The best plan of action for the players is to do things as quick as they can - if the Keeper can delay them for a couple turns (by, for instance, blocking a corridor with minions so the players can't get past), or the players can juke the Keeper early and be a step ahead, then the scenario is already over, and leaves a sour taste in everyone's mouth. The second edition made scenarios smaller, but kept a pretty slow pace. I'd have preferred a much faster pace (hacking through hordes of monsters easily). I had way more fun playing Hero Quest as a kid than I do playing Descent.
Mansions of Madness:
A One-vs-all game, rather than a true co-op. This game is a love-or-hate game. My group loves it, but you have to be committed to it, and you have to do everything you can to make it better for yourself and your players. The theme is fantastic, and all the missions are great fun. The expansions (both the single-scenario and bigger box ones) all improve a lot on the base game, particularly the more recent ones. Sometimes it gets a bad rap, and I thought I'd address a few:
Long set-up time: This is true, and is possibly the single biggest failing of the game, but one which is unavoidable. Set up involves: laying out the room tiles appropriately, Pulling the correct item, lock and keeper action cards out of the large deck, which vary depending on the scenario. Pulling out the correct clue cards, which vary depending on which *variation* of the scenario you're playing, and laying all those cards out in the correct room. If you get any of those wrong, the game breaks. You also have to have your players choose characters, and choose which starting items and stats those characters will have, as well as making sure you've got all your monsters, tokens and sundry other bits and pieces in easy reach. All of this is a mammoth task and can take a long time. The player in my group who owns the game always gets as much of this set up before we arrive whenever we play at his place - the tiles are laid out, the right cards are pulled out of the decks, and if he's playing the keeper, he's already placed them all appropriately. He's also super organised and has all the tokens and things in a sewing kit box with lots of little compartments. This makes playing it pretty frictionless. At worst, it's 10 minutes for the keeper player to read what he needs to do and seed the cards correctly. Making sure you do this will improve everyone's experience a lot.
Replayability: This really depends on how often you play. The base game comes with five scenarios, each of which has usually 3 story points, each with 3 variants. Often, the goal of the Keeper and the Investigators are significantly different between the variants. It's possible (and fun) to play the same map 3 times in the same day, with a different person playing Keeper and choosing different variants. By the third game, the Investigators have a basic idea of what's going on, but can still be surprised (particularly if they didn't read the other variants when they had their turn at Keeper). Doing this minimises downtime between games, as most of the set up is already done. If you played like this every week for 5 weeks, you'd quickly run out of scenarios. But if you're more like my group and play at most 2 variants in a session and only play once a month on average, then the game can last a while. If I went and played base game scenarios now, they'd seem fresh, because it's been a while. If you love it, this isn't an issue that will come up, as you'll religiously buy every expansion, all of which are glorious. The latest big box expansion changes some rules and the scenarios are in a very different style. I wouldn't buy it until you've gone through everything that came before.
Lack of any real "mystery" or "investigation" or meaningful clues: If the investigators are paying close attention, and you completely ignore the theme, it's true that a lot of the scenarios can be summarised as "go here, now go here, now go here, now kill this." Even once you're aware of that though, the theme is still thick like treacle, and there are always carrots dangling just out of reach. Often it's a question of "I know where I should go, and the fastest way to get there, but if I take the long way, I might get some useful weapons or items - Do I have time to take the long way?". Between this and the Keeper player actively hindering you, it can keep you on your toes. For the people who still don't find that satisfying, the latest expansion delivers all that in spades and has genuine mysteries, meaningful player interaction, and best of all - bluffing! This is great, but not recommended straight away, until you've got all the other mechanics well understood. The last time I played Keeper, I had three NPCs I could control - the Investigator's job was to kill a particular one, my job was to protect that one and kill one of the others or a player with a particular monster after certain conditions had been met. When the Investigators had deduced who they needed to kill early on, I was able to change my playstyle and tactic, completely fooling them and changing their mind, until I summoned a monstrosity from another dimension and ate their face.
Overall, I think Mansions of Madness is fantastic, and highly recommended *if* you can get over the above obstacles. The thing which hooked me was playing as an Investigator and walking into the Dining Room in this spooky mansion. The Keeper played a card that described horrible rotten-looking poisonous food on the table, which I felt compelled to eat - I failed my skill check, and was forced to eat the stuff, losing one point of health. This then allowed the keepr to play another card - saying that the damage was enough to break my arm and now I could only carry one item at a time. This was hilarious, but the idea of rotten nega-food being so bad for me that I fell down and broke my arm told a fantastic story. My other most memorable moment was when I was trying to mix ingredients to make an acid to get through the stone slab of a tomb. Three attempts in a row I put my ingredients together but rolled a critical fail on a skill check - which meant that I *drank* the acid. The third try killed me and one of the other players had to pick up and continue my work.
Welp, that was pretty long. Guess I should try going back to study now.