When I have an emergent idea or thought that I need to record, I usually do it on paper. I have a subscription to Evernote, Dropbox, Google Drive. I even keep a private Github repo available for simple text notes.
Still, the first place I go to mind dump is paper. Specifically, my Field Notes notebook. I love my Field Notes notebooks; they're a good size for pockets, they wear beautifully, and the paper feels great to write in.
Along with always carrying a notebook, I always carry a pen as well. I once preferred pencil but I found them unreliable for everyday pocket reliability.
I used to carry Pilot Precise click-top. I loved the fine line I could write with these pens. They were a huge improvement over ball point pens, in my opinion. Still, I wanted finer.
Eventually, I found the Pilot G2 ultra fine tip! This little guy is pretty much my standard pen now.
I also enjoy using the Zebra F-301, the Fisher Space Pen, and the Uni-Ball Signo.
Even though the Zebra is a medium tip ball point, it still feels pretty good. I'm not much of a ball point person so I don't really explore much.
The Fisher Space Pen is just a great pocket pen. Although, I get some odd looks when I pass through security checkpoints.
The Uni-Ball Signo is actually very interchangeable with the G2. It really depends what I have within reach.