Sometimes I do, sometimes I don't. If it's not a name I recognize, I check to see if it's a first question. (And frankly, I don't always remember whose names are whose, and people also change their names, so it's hard to keep track.) We've had so many trolls lately, I like to see if there's any history before I spend a ton of time. Also, if the question is brief or vague, I look back to see if there's anything relevant that will fill in the blanks. A lot of posters actually expect that members will know who they are or will look back, and leave out details on purpose because they feel they've posted them before. (In fact, some posters will say, "I've posted my story before" or "Many of your know my situation" so I do think there's an expectation that a number of answers will take that into account. So it saves everyone time, I think, if the advice is as on target as possible.
If it's a complex question, I will sometimes look to see if there are explanatory details in prior posts. I don't go back years and years, but if there's a title of a prior question that seems relevant, I do read it in order to (hopefully) do a better job of answering. A lot of times, the members responses are full of questions and requests for more information, so instead of doing that from the get-go, I look quickly to see if there's anything there. I think it also saves time for new responders who don't go back but do see a reference in another answer - I know I find it helpful when someone else answers with, "Well, I know that you have X children and that you were previously very candid about being in an abusive relationship…." I always appreciate the time they take to include those details if the questioner did not do so this time.
I do assume, if someone has posted before on the same topic, that it's important to her. So out of respect, I take all of her thoughts into account before I formulate my response.
If it's a question on recipes or products or where to vacation, I don't bother to look back because that info won't be relevant to this question.