Why is the last little part of a joint called a roach?

Search: roach

Why: On "1001 rules for my unborn son":

16. You are what you do, not what you say.

"On matters of style, swim with the current. On matters of principle, stand like a rock."
Thomas Jefferson

Thomas Jefferson's Airplane

And then, of course, I went rooting around for the origin of the name Jefferson Airplane (because - according to my brother - my favorite song when I was 5 was "We Built This City" by Starship), and I saw this:

The origin of the group's name is often disputed. "Jefferson airplane" is slang for a used paper match split to hold a marijuana joint that has been smoked too short to hold without burning the fingers - an improvised roach clip.

Answer: It comes from Mexican slang! Tobacco adulterated with marijuana or a cigarette stub of marijuana is called cucaracha (cockroach).

In Spanish, tabaco de cucaracha refers to adulterated tobacco generally.

Source: Wikipedia

The More You Know: So yes, there are a bunch of different versions of the song "La Cucaracha," but this is the one verse I learned when I took Spanish when I was, like, 10. I remember the first 3 lines, but not the 4th:

La cucaracha, la cucaracha
Ya no puede caminar
Porque no tiene, porque le falta
Marihuana pa' fumar

The cockroach, the cockroach
Can't walk anymore
Because it doesn't have, because it's lacking
Marijuana to smoke

It's some sort of satire about the Mexican Revolution, and lyrics and stanzas have changed and developed over time to fit the mood of the country. In general, the cockroach represents President Victoriano Huerta, a notorious drunk who was considered a villain and traitor due to his part in the death of revolutionary President Francisco Madero in 1913.