While Black Widow and Spider-Man have often times fought side-by-side, that friendly working relationship isn't present in every Marvel universe. In the Ultimate Marvel universe, the heroes don't much care for one another, it turns out. The animosity, it seems, stems from an incident that saw Peter Parker save the former spy, after which she rewarded him by poisoning him and stealing his tech.
In Ultimate X-Men #35 by Brian Michael Bendis, David Finch and Art Thibert, Wolverine is dealing with a mysterious Black Ops military unit that has been hunting him. Sustaining heavy injuries during an attack in Brooklyn, Logan unexpectedly crashes at Peter Parker's home in Queens. After his healing factor was done putting him back together, Wolverine and Spider-Man investigate the site of the ambush, where Wolverine learns that his pursuers had a copy of his Weapon X file. The documents contained within would hold details of Logan's life before he was brainwashed, augmented, and reprogrammed by the Weapon X military program.
With the always chatty Spider-Man accompanying him, Logan decides to cash in a favor and heads to Soho where he makes an unannounced entrance in Natasha Romanova's apartment looking for intel. Nat isn't happy with the surprise visit and her annoyance peaks with the arrival of Logan's "intern," at which point Spider-Man realizes he knows Black Widow and that she owes him $80. Peter recalls a previous adventure where he saved Natasha's life, after which, she not only poisoned him, but also stole his web-shooters.
The incident Peter refers to was in Ultimate Marvel Team-Up #14 (2002) by Bendis and artist Terry Moore and saw Black Widow's attempt to infiltrate the Latverian Embassy. She was eventually captured, but managed to escape with Spider-Man's help. As Peter swung her away, Natasha ended up poisoning him with a "widow's kiss," which knocked him unconscious. After stealing Spider-Man's web-shooters, Natasha's escape was interrupted by Nick Fury, who was more than annoyed. This all had been nothing but Black Widow's audition to join SHIELD, which later lead to her spot on the Ultimates.
The two spies depart while leaving an unconscious Peter Parker on the rooftop. This Team-Up series was meant to be an early introduction for readers to the new Ultimate universe, but the issues and the interactions brought up more questions than answers regarding continuity.
Spider-Man and Wolverine leave Nat's without any answers (or money) and the situation wouldn't get any better for Wolverine in the following issues. Although it wouldn't be the last time Bendis' Marvel Team Up series was referenced in his Ultimate comic stories, it's definitely one of the more memorable moments, especially considering Peter's opinion of Black Widow probably didn't improve after her actions during Ultimates 2.