This image appeared briefly in a recent TV show, among images of notable thieves. Can anyone identify who it is?
If I didn’t know any better I’d say is was an old friend of the family we called “Uncle Dennis” who was supposedly something of a bootlegger in an Irish gang in Chicago.
Frank Sinatra ?
I tried correcting out the distortion on the picture, to see if Google Images could find it. No luck, but here it is, in case it helps anyone:
My first thought was Dillinger, also, but in the photo on the Wikipedia page he seems to have a chin cleft.
Towards the end of his life, Dillinger had the cleft filled in. Even so, this pic doesn’t seem to be Dillinger. If you cover the mustache half, it doesn’t look at all like him. If you cover the clean cut half, it kind of looks like him. However, it seems to me, that in none of his pictures, did he ever have that much hair.
I say: Not Dillinger.
From that era, I’d think that it looks more like comedian Fred Allen, than Dillinger.
He’s listed as #19912. I wasn’t able to find anything quickly with that, but maybe someone else can.
Without checking the subsequent posts: Dillinger.
I’m going to be really embarrassed if it turns out to be Pee-Wee Herman.
Awhile back, ancestrydotcom was prominently using an unidentified old-timey portrait of a man in its TV ad.
I recognized him, because I’d just been reading a book about a crime he figured prominently in. Can you guess who he is? (don’t look at the url).
William J. Burns, famous early 20th century detective who cracked the Los Angeles Times bombing case, founded what became a huge detective agency and served as director of the federal Bureau of Investigation (forerunner of the FBI).
Ichabod Slipp? Hammond Egger?
It’s not Dillinger, and the plastic surgery he had in the last months of his life was ineffectual fakery at the hands of a quack.
I don’t think the person in the OP’s mug shot is a particularly notable person/criminal at all. Stock shot used for effect, and there are tens of thousands of old-timey mug shots available from the galleries.
Al Traina!
(Sorry, that’s a Café Society meme.)
^That’s not entirely facetious: the long SDMB Café Society nightmare of trying to ID the man in the Tonight Show Set photo (a man who turned out to be a not-particularly-famous person who at the time edited a low-circulation magazine) did bring home the lesson that even though a photo may seem to be of someone well-known, it may turn out to be of someone not famous at all. As Amateur Barbarian wrote above, it could simply be a shot from some stock archive.
Jaqen H’ghar.
Oddly enough there are a couple of pics of Jaqen’s actor on the Google Images page for the character, that do look somewhat not entirely unlike the Mugshot guy. 
OK, that was funny.