I'm glad I'm not the only person who has #3. For some reason, I seem to get miraculous insights into problems when I'm exercising, so I've taken to keeping a tiny pen and a couple index cards within reach at all times. While running, this has sometimes resulted in me crouching on the side of a street, scribbling madly while constantly looking for oncoming cars, but when I get back home and finally finish that tricky proof or implement that evasive idea into code, I find it is well worth the trouble.
I keep thinking I should get a voice recorder (my MP3 player can record, but starting up recording takes several seconds). But the sound of my own voice makes me uncomfortable, and I'm doubtful I would follow up.
I also get ideas e.g. when driving. A voice recorder could capture those.
Recently, I discovered while trouble-shooting something else that my old cell phone has a sort of half-*ssed recorder built in (requires extended button press; voice notes limited to 1 minute, despite having a 1 GB card in the thing). I imagine this feature is available on iPhone, Android, etc.?