-Hanlon's razor - I always start from the assumption that people seek the happiness of others once their own basic needs are met, then go from there. Helps me avoid the "rich people/fanatics/foreigners/etc are trying to kill us all [because they're purely evil and nonhuman]" conspiracies.
-"What would happen if I apply x a huge amount of times?" - taking things to the absurd level help expose the trend and is one of my favourite heuristics. Yes, it ignores the middle of the function, but more often than not, the value at x->infinity is all that matters. And when it isn't, the middle tends to be obvious anyway.
I'm not as smart as I like to think I am. Knowing that, I've gotten into a habit of trying to work out as many general principles as I can ahead of time, so that when I actually need to think of something, I've already done as much of the work as I can.
What are your most useful cached thoughts?
A few of the rules-of-thumb I've already pre-cached include:
That should be a reasonable but not overwhelming sample of the sorts of ideas I mean, and am hoping to evoke more of with this post.