Sorry for the late response. I think the other guys have covered the question well.
Yes, military pilots may have emergency procedures which they have to recall and perform from memory. So do airline pilots...but it depends on the type of plane (and sometimes the individual company).
For example, for the situation of a malfunction during engine start, for the companies that I presently train, one has that procedure as a 'memory' item and another does not. Same procedure, just different ways of handling the situation.
As aircraft get more dependable and reliable, fewer situations require responses to be memorized. Some of the companies that I work with use a method known as a Quick Reaction Card (QRC). This is a plastic covered single piece of heavy paper that has emergency procedures on it and is kept in the cockpit. For example, one QRC has 16 situations...before the QRC concept was instituted, all of these were memory items. Now, only 9 are, and the memory steps are reduced to the bare minimum. The idea is that the pilot can pull out the QRC and read and do it about as quickly as previously we would do things from memory. The added benefit is that the pilot doesn't make mistakes resulting from a faulty memory. Once the QRC steps are completed, then the pilot is directed to the main checklist to finish the procedure.
Here's a slightly different aspect of the memory item subject. Back in the day...and even now...I would ask the student what the very first thing he would do in the event of an emergency. The typical answer was that he needed to know what the situation was before he could answer. I then said that this wasn't necessary. Usually at this point the student is stumped and doesn't know what to say. So, I tell him..."Wind the clock".
"Wind the clock?" What does that mean? For one thing, today, the clocks are electric and don't need to be wound. What this means is simple. I don't really mean that the student should wind the clock...instead, I'm saying that he shouldn't rush off and do something without first pausing to consider what needs to be done. In other words, don't make the situation worse by doing the wrong thing. Slow down and think first. Then act.
Not that there aren't some situations that need an immediate response. I had enough situations when flying fighters where this was the case...speed was important because the situation was seriously bad. Such is life.
Even in the situation where I had to eject from an A-10, I still tried to get things sorted out first until it became obvious that this was something for which there was only one outcome. "Handles Raise, Triggers Squeeze". Boom. Out of Dodge.