In Star Wars IV: A New Hope, Luke sounds surprised to learn that Obi-Wan fought in the Clone Wars. I haven’t watched it recently, but I think he even said, “…but that was so long ago!?”
But according to the prequels, the Clone Wars lasted at least until Luke’s birth. So we’re talking about 20 years - not a lot of time at all!?
Imagine you grew up a farm boy in some podunk town in Backwater, Nebraska, where nothing ever happens. All your life you have never been further than 20 miles from the place you were born, and in that 20 miles there is nothing but corn. You are still in high school, and you realize your instructor used to be a Navy SEAL. And a secret agent. And walked on the moon. And advised the president. That is the level of excitement that Luke experiences when he learns who Ben is.
Things like Jedi and the Clone Wars, even though they are relatively recent events, they are distant enough from Luke's tiny existence to be legendary to him. Luke entering that larger world is a major part of the story of Star Wars. I don't think that audiences really appreciate that any more now that the prequels have been made.
When Obi-Wan mentions Luke's father, Luke asks, "You fought in the Clone Wars?" to which Obi-Wan replies, "Yes, I was once a Jedi Knight, the same as your father." They then proceed to talk about what happened to Luke's father. Luke never mentions how long ago the Clone Wars were, nor even expresses much surprise that Obi-Wan was involved. Over-all, he takes the news quite well. Here's a link to the clip.
It wouldn't really be surprising if Luke did think the Clone Wars were "so long ago." After all, when you've only been alive for 20 years, 20 years is a very long time. Most 20 year-olds today would say the '90s were "so long ago," too.
It seems my memory played a [Jedi mind] trick on me: The quote "But that was so long ago" is actually from the novelization of the movie that was authored by George Lucas before the movie came out (which is weird - the movie opened at the end of May 1977, but the book was published in November 1976!). As @Rogue Jedi pointed out in his comment, it was really ghostwritten by Alan Dean Foster.
While most of the book is in line with the movie, and material from the book later became canon ('Senator Palpatine' is mentioned for the very first time here!), there are changes. This appears to be one of them - movie Luke seems only mildly surprised to learn of Obi-Wan's involvement in the C.W., and doesn't mention the time aspect at all.
For more on the book, including some of the ways it differs from the movies, see this link: Star Wars: From the Adventures of Luke Skywalker
Beyond the fact that clone wars was quite a while before, and Luke is a young man, it is not unreasonable to expect that anyone left on the losing side of the war, would be dead. The Jedi were supposedly killed off, and Luke did not know Obi Wan was a Jedi at that point. The other major group of combatants - the clones - aged at double the normal rate and would be long dead, if they survived the war.
Another thing to consider is the fact that the clone wars were mainly fought on core worlds, and mention of the war on outer rim worlds would have been rare. And wouldn't you be surprised if an old hermit under a bridge told you he was a WWII General?
the Clone Wars lasted at least until Luke's birthtechicianlly Darth Vader (still in the human body of Anikan Skywalker) ended the Clone Wars before Luke's birth when he killed the Separatist leaders on Mustafar, which was probably hours before Luke & Leia's birth.