What is a solid basic strategy for surviving Arkham Horror?
People survive, and quite frequently as well. Here's a Google Doc of recorded games that a guy on the FFG forums has been keeping. It's got some pretty interesting statistics on it. 

https://docs.google.com/spreadsheet/ccc?key=0AliZyklaTCWzdEszdXpoRVJQNGltTU5wMi1qWEJnQkE#gid=2

As far a good strategies go, it's pretty simple. As you can see from the speadsheet, games with more investigators generally have a higher rate of success than games with less investigators. I've found that four investigators is generally a good number to play with. Any more and people can get bored with down time, any less and there's a good chance there's too much going on to take care of. It's also a nice middle ground for the number of gates that are allowed to be open, the number of monsters in Arkaham, the number of monsters in the outskirts, and you still only have one monster appearing per gate opening.

It's important to keep the gate count under control. Even if you can't seal a gate, make sure you have people going through gates so they have enough time to travel through and close without hitting the limit. Assuming one new gate per turn is a bit high, but it's a good rate to keep in mind for higher player games. I've had games end on the second turn in an 8-player game just due to unlucky Arkham encounters that opened gates. It can sneak up on you!

Which gates you seal/close is also important. It's slightly less predictable with expansion boards added in, but in the base set you have the 'Big 4': Independence Square, The Witch House, Unvisted Isle, and the Woods. These locations have gates that open significantly more frequently than other locations. If you close a gate here without sealing, odds are there's going to be another gate there soon enough, which adds a doom token to the track. Those are also the locations where Monster surges are more likely to happen. Conversely, locations such as the Historical Society, the Lodge, Hibb's Roadhouse, and the Science building, are targeted by Mythos Cards much less frequenty; it's less dicey to close those gates without sealing.

You may think it's important to have a dedicated monster killer (or at least someone good at it), and it definitely helps, but you can get by without it. Don't be afraid to spend a clue token or two to sneak past a monster guarding a gate so you don't have to deal with it. Also, don't forget that closing a gate removes all monsters with the matching symbol from the board.

Don't get sucked into spending all your clues to pass a check! I've seen so many instances where a player just decides, "Well, I've already spent two, might as well spend more..." only to burn their entire clue pile and have nothing to show for it at the end. Don't be afraid to fail a check! 

Have a decent amount of health before wandering into an Other World. Don't go into R'yleh with one Sanity and one Stamina. And please don't go into Unknown Kadath with one Sanity and one Stamina. If you're going for a seal, having more than five clues going in helps, obviously. The extra buffer isn't necessary, but it's comforting.

Some people will swear by getting retainers from the newspaper or bank loans to get cash to buy weapons, but more often than not my group can get by just fine with our starting equipment and the odds and ends we pick up while playing. Encounters spent trying to get money and good items could be spent getting clues, either off of the board or from random encounters. It's up to you to decide what would be more useful.

Most importantly, have fun!