last night, I felt like something tapped my arm but there was nothing. What would cause that?
Most likely it's some sort of combination of tactile hallucination and muscle twitching/skin contraction. It's quite common to feel random impulses like that, so much so that we normally block most of it out. But when there are fewer distractions (say, at night, when there's less visual information due to darkness and -usually- less audio information due to things quieting down) we have a tendency to pay more attention and start noticing them more. Probably one of the most common is a faint breeze or skin contraction causing a few hairs to rub together, creating the sensation of a bug crawling along the skin (thanks to your mind filling in the gaps of what is "most likely" causing the feeling).
Various muscles can start twitching for a variety of reasons, and if it's close enough to the skin it can feel similar enough to an external force that your brain just "helps out" and makes you perceive it as definitely being touched. Because the brain likes to figure things out, it supplies an answer/explanation to something that wasn't even a question to begin with.
We work off of partial and incomplete information under most circumstances, but it's beneficial from an evolutionary standpoint to "fudge" the rest of the details instead of waiting around to get a more complete data set ("Is that a tiger lying in wait or just some shadows? I don't know, but I'm not sticking around to find out for sure!").
Also what delphonso said regarding sleep/pre-sleep sensations. There are a number of processes going on in the body during sleep preparation and active sleep that can result in various curious experiences.