Mafia members (at least Italian mafia) are admired by Americans bacause they go their own way in society, taking risks and making big money in non-traditional ways. Yes, they rob and kill, but they live by a certain code of honor as well.
The fact that they'll probably die or go to prison adds a romantic edge to their lives...
American bank robbers of the 1930s, and cowboy outlaws of the old West were also attractive to some people for those same reasons.
(Note: The word "outlaw" is a very old English word and refers to a person who lives outside of the law of society.)
Nowadays, the heroes of TV shows such as "Breaking Bad" (a college professor turned drug dealer) and movies like the Dark Knight series seem to celebrate the bad guy equally or more than the good guy. In the Dark Knight, people seem to identify more with "The Joker" than Batman.
Some people believe this concept also explains the popularity of Donald Trump ! (G.K)
go their own way 我が道を行く
in non-traditional ways 非伝統的な方法で（強盗、殺人を指す）
code of honor 礼儀、作法
romantice edge ロマンティクな香り
for those same reasons 同じ理由で
drug dealer 薬の密売人
equally or more than 〜 〜と同じようにいやそれ以上に
identify more with 〜 〜とより一体感を持つ