For some types of questions educated guessing is certainly an option, for example, Data Sufficiency, questions with Variables in the Answer Choices, and questions that ask which options must be true. For Data Sufficiency there is a whole strategy for deciding what is most likely to be true. It is not really even guessing since you can usually evaluate at least one of the two statements. This can be pretty reliable and even though you have not fully mathematically proven that the answer is "C" or "D" or whatever you can actually have more than a 50/50 chance on these problems.
However, your standard problem solving question is not a great place for educated guessing. The truth is that it can be very hard to know which choices to eliminate when staring at a problem solving question that you are unable to complete. Remember that on these types of problems educated guessing is still guessing. There was a pretty good discussion on this point a year or so ago and the experts decided that anything more than 30 seconds to try to eliminate choices on a typical problem solving question is just too long. Better to invest that time in the problems you can get right.
You should be able to apply the technique that Jim discusses in less than 30 seconds. If so use it. Remember that for problem solving questions where the answer choices are actual numbers - you either work the problem and get one answer that you are confident in and you find that answer in the choices --- or you guess, and whatever the form of your guessing it is still guessing.
As to which answers are more common I do have one rhyme that can help you. "Take the E out of Geometry in Data Sufficiency." This is because you can usually do more with Geometry than you think and the correct answer is rarely E for these type of data sufficiency problems. In other words, if you need to make an educated guess on data sufficiency geometry avoid choosing E.
Other than that there are no trends in answer choices that I know of... If there were I suspect that the test writers would soon correct this.
