The only person I know to regularly write even large programs by hand is Donald Knuth. This includes the early heroics of his college days ([1][2][3][4]). It includes TeX and METAFONT which he wrote in the 1980s over several months, before typing them in. (Corroborated right here on HN [5] by David Fuchs [6] who worked very closely with Knuth on TeX.) I'm pretty sure from looking at some his recent programs [7] that he still writes by hand.
Of course as a programmer Knuth is sui generis and has developed his own idiosyncratic style of programming over the decades, different from the rest of the world (consider his idea of Literate Programming). He thinks differently, tends towards monolithic rather than modular, and is always in book-author mode even when writing programs. He has some abilities and disciplines that more than make up for what some others would consider defects. What works for him may not work for others. Still, it would be interesting to hear of more people's experiences writing by hand.
A couple of months ago I wrote a small program in an assembly-like language for fun, and I felt that writing out the first couple of drafts by hand was quite helpful, and prevented me from jumping to an implementation too quickly.
[1]: http://ed-thelen.org/comp-hist/B5000-AlgolRWaychoff.html#7
[2]: http://archive.computerhistory.org/resources/text/Knuth_Don_... (Note "half-true" on the cover page is penciled by Knuth!)
[3]: http://www.metafilter.com/122701/STORIES-ABOUT-THE-B5000-AND...
[4]: http://archive.computerhistory.org/resources/text/Knuth_Don_...
[5]: https://news.ycombinator.com/item?id=10172924
[6]: https://www.tug.org/interviews/fuchs.html
[7]: http://www.cs.stanford.edu/~knuth/programs.html (I've generated PDF versions: https://github.com/shreevatsa/knuth-literate-programs/tree/1...)