We don't know whether or not Obi-Wan came to regret his decision to let Vader live, but we do know that he definitely wanted Luke to kill Vader. In fact, he explicitly says that if Luke doesn't kill Vader, the Emperor will win:
You cannot escape your destiny. You must face Darth Vader again.
I can't kill my own father.
Then the Emperor has already won. You were our only hope.
- Return of the Jedi
However, Obi-Wan was obviously and completely wrong about that, because Luke's mercy towards Vader when Vader was defenseless is exactly what saved Luke from the Dark Side and led to the Emperor's defeat. And Obi-Wan is clearly quite pleased to have been proven wrong:
And as DVK's answer here states, when Obi-Wan left Vader maimed and helpless on Mustafar, he made a conscious decision to let Vader live:
Obi-Wan looked down. It would be a mercy to kill him.
He was not feeling merciful.
He was feeling calm, and clear, and he knew that to climb down to that black beach might cost him more time than he had.
Another Sith Lord approached.
In the end, there was only one choice. It was a choice he had made many years before, when he had passed his trials of Jedi Knighthood, and sworn himself to the Jedi forever. In the end, he was still Obi-Wan Kenobi, and he was still a Jedi, and he would not murder a helpless man.
He would leave it to the will of the Force.
- Novelization of Revenge of the Sith
As this passage makes clear, Obi-Wan didn't really consider killing Vader now to be a viable option - it would have gone against everything the Jedi stood for, and the whole point of Obi-Wan's fight with Vader had been Vader's betrayal of the Jedi and their principles. If you defend your principles by violating them, you're a hypocrite, and you do more harm to your position than any opponent ever could. If you avenge the murder of defenseless people (like the younglings, or Sand People women and children) by murdering a defenseless person, you have no integrity and might as well join the bad guys. In short, Obi-Wan knew he couldn't kill Anakin because if he did, he would become Anakin.
Furthermore, Obi-Wan's decision wasn't entirely a choice between killing Vader or letting Vader live; the choice is actually between killing Vader or letting the Force decide. Keep in mind that one of the most frequently used words in the Star Wars saga is "destiny". The Jedi (and even the Sith, in most cases) know that destiny, more than personal decisions, is the determining factor in the course of events. Obi-Wan knew that Vader's story would play out exactly as it was supposed to, and nothing that Obi-Wan did would change that. Although he couldn't see it at the time, in the heat of the moment, Anakin's fall didn't change the fact that he was indeed the chosen one, and would ultimately bring balance to the Force - Obi-Wan just didn't realize that the time hadn't come for Anakin to bring balance to the Force, and that was destined to happen decades later, when Anakin's love for Luke triumphed over his loyalty to Palpatine.
My answers here, and here, and here, and here, and here, as well as Thaddeus' answer here, go a bit deeper into the Jedi perspective on killing unarmed opponents - it is especially relevant that Luke's decision to show mercy to Vader at the end of Return of the Jedi is the very thing that keeps him from falling to the Dark Side and inspires Vader to redeem himself and save Luke.