Both Tom and Daisy Buchanan cheat on each other and carry on affairs in Fitzgerald's classic novel The Great Gatsby. Tom proceeds to carry on an affair with Myrtle Wilson and even rents an apartment in the city where they spend time together away from their spouses.

After Daisy is reintroduced to her former lover, Jay Gatsby, at Nick Carraway's modest home, she proceeds to carry on an affair with him. Jay Gatsby believes that he will convince Daisy to eventually leave Tom and even stops hosting his magnificent parties. Daisy cheats on Tom by routinely visiting Gatsby's home in the afternoons. Gatsby even dismisses his servants to prevent gossip regarding his affair with Daisy from spreading to East Egg.

After Tom Buchanan discovers that Daisy has been cheating on him, he becomes furious and conducts an investigation into Gatsby's shady business affairs. Tom learns that Gatsby is a notorious bootlegger who is highly connected in the criminal underworld. Tom eventually exposes Gatsby, and Daisy refuses to leave her husband even though Tom is an unfaithful, despicable man.

Yes, we find out that Daisy has been coming over to Gatsby's house most afternoons after their meeting.  Consequently, Gatsby stopped having parties, and he dismissed all his staff, hiring new servants who would not gossip.  In Chapter 7, he tells Nick,

Daisy comes over quite often--in the afternoons.

It is clear that Daisy and Gatsby have had a physical relationship because Daisy flaunts it in front of Tom.  At her own house in the presence of her husband, she kisses Gatsby.  Gatsby, also, is so sure that Daisy will leave Tom and go with him.  When Tom got wind of the affair between Daisy and Gatsby, he did some investigation of Gatsby's past and present business and found out that Gatsby was involved in bootlegging and some other unsavory business dealings.  All these clues let us know that Daisy and Gatsby have been having an affair.

Another more minor episode of cheating is Nick's relationship with Jordan.  Although he has a girlfriend back home to whom Nick writes faithfully, Nick pursues a romantic relationship with Jordan while he is in New York.  Even though he does not actually have an affair with Jordan, he does express interest in her while at the same time signing his letters "love, Nick" to his hometown girlfriend.