The thing that I have been most surprised by is how much NTs like symbols and gestures.
Here are some examples:
Suppose you think your significant other should have a cake on his/her birthday. You are not good at baking. Aspie logic: "It's better to buy a cake from a bakery than to make it myself, since the better the cake tastes the happier they'll be." Of course, the correct answer is that the effort you put into it is what matters (to an NT).
Suppose you are walking through a doorway and you are aware that there is someone about 20 feet behind you. Aspie logic: "If I hold the door for them they will feel obligated to speed up a little, so that I'm not waiting too long. That will just inconvenience them. Plus, it's not hard to open a door. Thus, it's better for them if I let the door close." To the NT, you are just inconsiderate.
Suppose you are sending out invitations to a graduation party. You know that one of your close friends is going to be out of town that weekend. Aspie logic: "There is no reason to send them an invitation, since I already know they can't go. In fact, sending them an invitation might make them feel bad." If your friend is an NT, it's the wrong answer. They want to know they are wanted. Plus, it's always possible their travel plans will get canceled.
In each of these 3 examples the person with AS is actually being considerate, but would not appear that way to an NT.
Suppose you are sending out invitations to a graduation party. You know that one of your close friends is going to be out of town that weekend. Aspie logic: "There is no reason to send them an invitation, since I already know they can't go. In fact, sending them an invitation might make them feel bad." If your friend is an NT, it's the wrong answer. They want to know they are wanted. Plus, it's always possible their travel plans will get canceled.
There's also a difference between Ask and Guess cultures in this kind of things.
Followup to: Do you have High-Functioning Asperger's Syndrome?
LW reader Madbadger uses the metaphor of a GPU and a CPU in a desktop system to think about people with Asperger's Syndrome: general intelligence is like a CPU, being universal but only mediocre at any particular task, whereas the "social coprocessor" brainware in a Neurotypical brain is like a GPU: highly specialized but great at what it does. Neurotypical people are like computers with measly Pentium IV processors, but expensive Radeon HD 4890 GPUs. A High-functioning AS person is an Intel Core i7 Extreme Edition - with on-board graphics!
This analogy also covers the spectrum view of social/empathic abilities, you can think about having a weaker social coprocessor than average if you have some of the tendencies of AS but not others. You can even think of your score on the AQ Test as being like the Tom's Hardware Rating of your Coprocessor. (Lower numbers are better!).
If you lack that powerful social coprocessor, what can you do? Well, you'll have to run your social interactions "in software", i.e. explicitly reason through the complex human social game that most people play without ever really understanding. There are several tricks that a High-functioning AS person can use in this situation: