It's a word you hear quite often on the HBO mobster series, The Sopranos.

It means nothing. As in, "Did you get any from that chick last night?" "Nah, I got stugots."
It's also used to indicate someone that has a lot of balls, usually followed by a crotch grab.

The characters use it as their own little swear word, much like teenagers using the word fuck or dick.

Supposedly it's an Americanization of "esto cozzo", translating to "this cock."

Tony Soprano's boat on the show is named The Stugots.