I did a lot of looking around online to see what sort of scores I should be aiming for, and saw a lot of talk about the 80th percentile or somewhere around there. This is an extremely ambitious objective for most people taking the test (this isn't even just my opinion, but we're all good at math here so I don't have to explain that). First remember what percentile means, and then remember that usually 50% of people don't fail a test. You should also keep in mind that you're really only competing with other people about to apply for a PhD in math. Doing better than half of them is nothing to sneeze at, and is good enough for most universities if the rest of your application is looking good.
There are a couple of cases when perhaps you should demand more of yourself: 1.) If you're uncertain about your application an incredible grade on the subject GRE would give someone a reason to give you a chance. 2.) You're really planning on going to Princeton or something and won't settle for less. 3.) You are exceptionally talented at solving tricky multiple choice questions in one try really fast.
Otherwise, in my opinion, trying to get every question right can actually mess you up pretty bad. I learned this from the practice tests I did. I know that from a probabilistic perspective you stand to benefit from guessing if you've eliminated at least 2 choices, however I think this reasoning is flawed because your guess will be far from random. The options provided are intended to trick you if you haven't investigated every detail of the problem. I actually considered applying some elementary game theory here and making a list of the questions I plan to guess on, and the remaining choices of each one, then using a randomizing technique on selection from there. But ultimately that would just be another way to take time away from the rest of test.
Which brings me to my next point. Even the ones you know for sure are written in such a way that you can mess them up if you aren't careful. If you try to answer all 66 questions, you risk rushing yourself and making a lot of mistakes. And a multiple choice test doesn't care if you understood the relevant concepts of a problem. It's also not obvious if you've made a mistake. You can have a good deal of confidence about your wrong answer when you've failed to observe something.
At first I was all about trying to get a jaw-dropping perfect score on this exam. [I have a 3.986 GPA from the start of my BA up to now (one year away from the masters in a ba/ma program), I got into a research group this semester that only excepted 12 people out of thousands of applicants in New York City, I tutor all levels of undergrad math and started a new tutoring section at my job just so I could cover abstract algebra, et cetera etc., ... I get a lot of respect for my math abilities.] But I discovered that an 80th percentile score was not a wise target for me, unless I were to dedicate weeks to practicing timed multiple choice questions (of which there are a limited amount).
The point is, it's not like you'll miss that 80th but still get the 75th: you could rush your way through a ton of errors and end up in the 30th, when if you were more realistic you could have got a solid 60th. When you narrow your target, you're more likely to miss it. And those wrong answers are the hostages. It's like if you were a well-hidden assassin with a clear shot at a fascist dictator, but instead of pulling the trigger you jump on a time-traveling helicopter to try to take out Hitler. Next thing you know it's 7578 and octopi have domesticated humans and your stray bullet kills your great^215th-grand-daughter. Only not neaerly as bad as that.
Anyway, my strategy was as follows:
Read the entire test once, rather quickly but attentively, and notate the apparent difficulty level of each problem on a scale of 1 to 3. Base this not on how hard of a topic it is, but on your insight on how to approach it, and on how long you think it would take to do. (my method is a square around the 3s, a triangle around the 2s, and don't do anything to the 1s.) Don't be afraid to only mark half the test as easy. If you get half the possible raw score you're already over the top of the curve.
After the read-through, go back and start doing the 1's, skipping the rest.
If you get an answer that isn't a choice, or if you get stuck, circle the problem and move on. [Important: don't jump to conclusions at this point. Circle it to come back to later.] After you finish, go back and take a look at the 2's, but be more liberal about skipping when you feel you are getting hung up or not noticing something. Then go back and take another shot at those circled problems, before you even look at the hard ones. Your chances of catching a mistake in something you attempted earlier is better than your chances of correctly doing something that you are uncomfortable with, and faster than doing an in-depth analysis on something very difficult.
Finally take a shot at those boxed ones, along with the skipped triangles. Some of them may be things you have no idea what they're talking about, or that reference material you never even learned, so don't waste time when that happens. Do be sure to read through it though because sometimes familiar concepts are disguised in strange formats/language. And sometimes doing just a natural first step makes something obvious fall out.
Then go back to the beginning and quickly decide on which ones you can resolve in the remaining time. You should have a good ability to do this at this point because you've messed around with all of them by now. Isolate some of those bastards and take them out. But stay focused. This would also be a good time to guess but only if you really have thought through the solution and are very confident of the form the solution should be taking. Don't be tempted to go in and try to do the rest of them really fast like you're some kind of genius. You'll probably just fall for every trap along the way and mess up your confidently-collected points.
Note that my method still requires you to move at a fast pace, especially since you have to go back and 2nd-try a bunch of questions. So this still requires a lot of practice and studying, I just think it has more reliable results than trying to destroy the thing. Also when you study, you should be learning what your strengths and weaknesses are, and using that information wisely.
Finally, pay a lot of attention to the practice tests. Try one or two where you try to to answer them all, in a timed session, and try to get them all right. You'll probably see what I'm talking about. If not, disregard...
So that's my 2-cents. I just took the test today so I'm still winding down from the obsession over it. Plus I drank 3 red bulls and I'm bouncin off the walls. I answered 39 questions, but I am quite certain I got at least 35 of those. This puts me in a range of about 660-710 if I use the conversion chart from the practice test, or 57-68%. I won't know for sure until May 15, but I don't feel like I took a lot of chances, I think my answers were solid.
I'm not looking to go to an IV league place personally, and according to my graduate advisor at Hunter College there are places well inside the top-40 schools to whom my application is going to look very strong.
I hope this helps people out. I think there needs to be more discussion about the 50th percentile on here. You don't need to have your PhD in nonassociative algebras to figure out that most of the people taking the test are among that population. Also it is not the case that 70% of people who apply to math PhD programs have to settle for jobs cleaning all the bathrooms at grand central station with their own toothbrush.