Hi BlueLotus, despite what other people say, I don't think that the numbness just disappears by itself. That is not due to the legs becoming used to it... they're just positioned in a way where they don't become numb.
(Sorry if the following makes you feel queasy.) There is a bundle of nerve that runs down from the spine to the back of each legs, called sciatic nerve... google it to see the anatomy. I think that many people, when they sit, end up compressing this nerve just past the sitting bones. (Also google this, they're the bottom two points of your pelvis bone... which are seated on a ground when the pelvis bone is aligned straight up.)
You can easily avoid the numbness by sitting on a bare ground (which requires the flexibility around the hip joints though, but not impossible)... but with a cushion, it's a bit challenging. You want to sit on it in a way where the nerve doesn't end up compressed. Most teachers say that you do this by sitting right on the edge of cushion, just at the sitting bones, instead of on your thighs.
You'll just have to experiment with it. I found out that when I sit in a Burmese position, if my left leg (which I broke a couple years, in an unrelated incident) wasn't placed to the left far enough, it would end up numb. If it was placed far enough, then there's no numbness. That is only a couple millimeter difference. The way that I sit, the heel of each foot is almost right in front of each other.
In half-lotus, it's a bit more challenging. I think that you should be able to sit in Burmese style with both of the knees touching the ground (it's possible, and very easy to do once you have the flexibility), before doing the half-lotus. The flexibility in the hip joint is very important, and make sure that the bottom of your lower foot (especially the heel bone) isn't pressing too hard against the bottom of your opposite thigh, which would end up compressing the nerve.
It's also helpful, after placing the leg in half-lotus, to push off the ground a little bit, and then rotate the hip joint to loosen it up (also raising and lowering the knee several times, to loosen the hip joint), before setting the sitting bone back on the cushion. The half-lotus will feel much more comfortable. Throughout your meditation, make sure that the muscles around that joint don't tense up too much... pay attention, and let go any of tension that builds up there; keep it relaxed.
I think that half-lotus is definitely worth learning. It takes much less effort to sit straight up than in Burmese position (though it's also easy in the latter, once you learn how). You really need to develop good flexibility for it... do some stretches daily, especially around the hamstrings (you only need to do this gently)... I just figured this out by experimenting. Or else it's too uncomfortable, and you'll risk hurting yourself.
I only started sitting regularly around six months ago... my left knee was way up off the ground (in Burmese position), because of my broken leg. Around few months later, I could sit with both knees on the ground. And now, I can sit in half-lotus with my right leg (for around an hour)... but haven't tried that with my left leg, yet. I only try to sit in half-lotus with that one for around 15 or so minutes.