The Fantastic Four did fight mobsters on occasion in the 60's, but since it's been rare. I know Hammerhead tried taking them on with an exo-skeleton armor suit during the John Bryne run, I believe.
When Matt Murdock's identity was leaked to the media/world during Bendis' run, several hit-men tried to kill him, including Boomerang and Shotgun.
Crossfire once put a contract out on Hawkeye's arm; not him, his ARM. He likely figured it was a better revenge to make him unable to be an archer anymore than outright killing him. That's arch enemies for you!
At one point in the 90's, Trapster framed Spider-Man for murdering low level thug Joey Z in his webs, and a very high bounty was put on his head for capture. This led Peter to "retire" his Spider-Man persona and don four alternate identities to battle crime and clear his name in a story called IDENTITY CRISIS. These were Hornet, Ricochet, Dusk, and Prodigy - at least the latter was a suit co-created by his ally, the Prowler. Spider-Man ultimately cleared his name and the bounty was dropped, but Mephisto adopted this costumes and gave them to aging Golden Age hero the Black Marvel to use in his quest to avenge a prior failure. He bestowed the costumes onto four new youths and that was how THE SLINGERS were born. Various mobsters have offered bounties for anyone who kills Spider-Man, naturally.
I am fairly certain Frank Castle/The Punisher has had various contracts out on him, and he's often made target practice of assassins. Elektra and Wolverine as well. Elektra is herself a professional assassin.
While not really a hero, Taskmaster has worked with the federal government on occasion, including helping train John Walker to replace Capt. America and then training heroes/soldiers during Stark & Osborn's Initiative program. When work leaked that he'd been a mole for Steve Rogers the entire time, a bounty of one billion dollars was placed on him and virtually every evil organization in Marvel sought to collect, from AIM to HYDRA to ULTIMATUM to the Secret Society, Serpent Society, Cyber-Ninja, and even ones never seen before. It was ultimately a ruse by a secret mastermind, and after Taskmaster killed him, the contract was presumably cut off.
Arcade is also a contract assassin, albeit an unsuccessful once since he started taking on heroes. He's sought to collect on hits on Capt. Britain, Spider-Man, and the X-Men, among others (like Tony Stark or the Thing).
In terms of professional hit-men, they're a dime a dozen in Marvel besides Blackout and Arcade. Many of them have had the displeasure of fighting heroes willing to kill, like Wolverine and Punisher. Sabretooth used to work for hire, as did Tiger-Shark. Kingpin naturally employs Bullseye to kill for him, and even very briefly, the Vulture (and the newest Hobgoblin recently). Some have obvious names, like "Bounty Hunter", "Hitman", and "Warrant". The professional mercenary Paladin has on at least one occasion been willing to accept an assassination contract due to a lofty payday and acceptable target.
Intergalactically, Gamora has accepted contracts and earned her title of "deadliest woman in the galaxy" that way. The Skrulls have been willing to put alien contracts on the Four on occasion. At one point a "Galactus Revenge Squad" type group went after Silver Surfer.