Ross and Monica's relationship is strange, but it is not incestuous. In response to Monica's claim that she knows when Ross lost his virginity, she subsequently admits in a later episode that she doesn't. She knows that was his first time with Carol, but no one else seemed to have noticed. This implies that either Ross was very discreet about his sexual activities or that everyone else was being very polite about what would be an awkward topic of conversation.
They also weren't friends as much as partners. Although they were both involved with other people, neither of them wanted to get involved with the other person's partner. When Monica tells Ross that she thinks he's attractive, he replies "You think anyone else does?" This shows that even though they were both committed to other people, they still had feelings for one another.
In conclusion, Ross and Monica's relationship was strange but not incestuous.
Ross is divorced and freshly alone in the first episode after his wife, Carol (Jane Sibbett), discovers she is a lesbian. Later in the series, he dates Rachel, but they break up when he sleeps with another woman the night they decide to put their relationship "on hold."
He starts dating Sarah again in season five, just as her husband, Jeff (Sam Huntington), comes back from war alive and well. But they break up when Sarah realizes that Ross has been cheating on her with Rachel all this time.
It turns out that they are all still friends and get together for Christmas 1998. After getting into some trouble with the police due to some stolen goods that were in his car, they plan to skip town until they realize that they owe money to some people who want to kill them. So instead, they go on the run like criminals until the cops can't chase them any longer. At the end of the episode, "The Gang Goes to Hawaii", they show up at Carol's house to tell her that they are going to Hawaii without her so she can move in with her new girlfriend. Then they all have breakfast together before they go their separate ways.
Ross returns in several episodes over the next few seasons as a regular cast member. In these episodes, we see him dealing with his ex-wife's death, raising Amy alone, becoming a father again through artificial insemination, and more.
Monica was a senior in high school at the time, and Chandler was Ross' freshman college roommate. Their relationship, however, had a bumpy start when Monica developed an infatuation on Chandler and overheard him refer to her as Ross' "fat sister." This offended Monica, who then ended their friendship.
Years later, after both graduates from university and got jobs in California, they decided to give their romance another try. This time, though, Chandler didn't want to wait so he asked Monica to marry him. She said yes! They then spent their wedding night arguing about which one of them should drive back home. Finally, Monica won this battle of wits and pulled over to sleep in her car while Chandler returned home.
Monica then realized she wasn't ready for marriage and broke up with Chandler. But despite this, they still love each other very much and are still good friends today.
Here's how they explained their marriage at different times:
Chandler: I married her because I thought she was beautiful and I wanted to marry her.
Ross: If you were just dating my sister, you wouldn't be marrying her. You'd be dating her.
Chandler: [about why he married Monica] It was right before my birthday and I wished on a star. A fat one.
Ross and Rachel met in high school, and despite the fact that Ross was in a higher grade, he developed a crush on her, albeit he never made a move. Rachel lost contact with Ross and Monica until a year before the pilot episode, when she ran into Monica and eventually moved in with her after fleeing her wedding.
They end up dating again, this time as friends, but when Rachel learns that Ross is engaged to Jennifer, she gets jealous and they break up for good. However, they get back together at the end of season one.
Their second breakup was much more painful for both parties involved, and it took them several months to work things out. By the end of season three, they got back together yet again.
In the fourth season, they finally admit their love for each other and are about to kiss when Joey interrupts them. He tells them that they're being watched by Officer Donna Pinciotti (the daughter of Detective Frank Pinciotti from 1998 series Homicide: Life on the Street), who is still angry about how they treated her father. She's also there to arrest Rachel for drug possession. However, due to Monica's intervention, Rachel avoids going to jail and agrees to do community service. Later on, it is revealed that Officer Pinciotti has resigned from the force and moved to France.
Ross and Rachel marry in the season 5 finale, "The One in Vegas," after getting drunk in Las Vegas. Rachel becomes pregnant at the end of Season 7 at Monica and Chandler's wedding. In the second episode of Season 8, the father is revealed to be Ross, and Rachel informs him in the next episode. They break up for two seasons before deciding to try again and marrying each other in April 2001.
Although they don't mention it by name, this is probably what happened to their marriage after Phoebe and Mike broke up. They actually do say "We're still friends" right before they kiss, suggesting that maybe they ended up back together. But since they also say "I love you" later in the same scene, maybe not?
In any case, they do get married in Friends so we can assume that this part of their story ends happily ever after.
However, their marriage was not real — it was only used as a device to tell stories about people getting married. So even though they get married in the series, this doesn't mean that their marriage was valid in the eyes of God.