Betty & Barney Hill were an interracial couple from Portsmouth, New Hampshire, USA who claimed they were abducted by extraterrestrials on September 19, 1961. It has become one of the better known alien abduction cases being widely pubicised and featuring in countless books about alien spacecraft and abduction. For a more thorough analysis of this case the Wikipedia Barney and Betty Hill article is highly recommended.
Basically, the Hills were driving home from a holiday at Niagara Falls when they observed a light in the sky. It is also suggested that the Hills arrived home 3 hours later than they should have, but interestingly the Hills hadn't noticed this "fact" on the night. The rest of the story comes out over the ensuing months and even years, including the Hills "realisation" that there was any "missing time" at all.
A compelling aspect of this case, as far as proponents of alien abduction are concerned, is that the details of the abduction recounted by the Hills are extremely comprehensive, and that whilst not always in agreement with each other, more often than not the account told by Betty matches the account told by Barney. The Hills were respected members of the community and people would often comment that they seemed very sincere in their recall of the events.
On the other hand, it should also be noted that the Hills story evolved over time. They didn't just arrive home that night and start discussing exactly what had happened to them and why they were 3 hours late arriving home. Details emerged over time following dreams, hypnosis and importantly discussion between the Hills. The story was recounted and told many times by the Hills themselves as well as in books and newspaper articles.
Unfortunately for those who want to believe that extraterrestrials are visiting the Earth and abducting people, this case doesn't provide any evidence at all. There is nothing physical to corroborate the Hills account of events. This case actually provides more evidence for the Malleability of Human Memory than it does for extraterrestrial abduction.
The Skeptoid Podcast by Brian Dunning presents a good well-reasoned view of the Betty and Barney Hill case. We highly recommend you check out this episode and others. Skeptoid podcasts are short and easy to understand.
For some balance you might also enjoy reading this article by Kathleen Marden on Where the Debunkers Went Wrong. We can't corroborate the information presented in the article. It is simply offered as is for your perusal.
I have no doubt that the Hills' believed they had been abducted by aliens. I don't suggest that they had knowingly fabricated the story. What I do believe has happened is that over countless telling and retelling, the story has evolved in both complexity and in the memories of Betty and Barney. The malleability of human memory is a powerful thing. It leads to so many misunderstandings and has very real consequences every day.