Most of the fiction that role playing games pulls from is rich with a history of heroes solving difficult riddles. The most famous of these is probably from Greek mythology, the riddle of the Sphinx:

What goes on four legs in the morning, on two legs at noon, and on three legs in the evening?

In stories and legends, the hero generally solves the riddle where nobody else has succeeded.

The problem is that players are real people, and real people often get stumped on riddles. There's nothing more frustrating for a player than having the action stop completely while they try to puzzle out the answer to a riddle. You give them hints, with subtle indications that the answer is obvious (it's obvious to you, because you created the riddle).

There's a disconnect between the use of riddles in legend and fiction, and the use of riddles in RPGs.

In legends and fiction, riddles are an exciting dramatic tool. A riddle so hard that hundreds of people have failed to solve it, and having failed are destroyed, is solved by the hero against all odds. What makes it even more exciting is that the reader often fails to solve the riddle, and so the hero's triumph is that much more amazing to us.

In role playing games, the players are both hero and reader. They can get stumped on the riddle, and fail to solve it. But as the hero, their role is to solve the riddle and win through against all odds.

How do we resolve this?

With Comedy

Make the riddles part of an ongoing joke in your campaign. Every dungeon has an area controlled by a sentient artifact of some sort, all placed by the same mad mage centuries before. The riddles are arbitrarily hard, and the answers make no sense. All the answers are also available elsewhere in the dungeon. After all, the orcs patrolling need to get past the artifact on a regular basis, and can't be bothered to remember the answer, so they probably have it written down.

The key with this approach is that actually solving the riddle is not necessary for the story to advance. They may have already found the orcs carrying a sheet of vellum with the phrase, "A really skinny elephant" written on it, and then later encounter the artifact that asks, "What is gray and weighs two pounds". They get a good chuckle out of the silly riddle and move on.

This approach doesn't work for all campaigns, but if it works for yours you'll have your players looking forward to both hearing the riddle in the next dungeon, and figuring out where the answer is hidden.

With Drama

The hero is supposed to solve the riddle. So they do.

This technique was used effectively in a LARP I played in. There was a bridge being guarded by an ogre with a huge club. He offered to let anyone pass who could solve a riddle. The way he hefted the club, it was pretty obvious that anyone not solving the riddle would get hit over the head with it.

He would dramatically intone his riddle, and wait for an answer. He had a different riddle for each person who wanted to cross, and they were all real puzzlers. One was along the lines of, "A man in a village walks five miles to the next village and finds it deserted, except for a cow and a chicken. He returns to his own village and tells his wife what he found. What does the man have for dinner?"

Someone answered, "chicken with milk". The ogre paused, and exclaimed, "That's right, you may pass!"

We found out after the game that any answer would have done, no matter what it was. This worked because of our belief in there being a right answer, and our believe in the negative consequences of answering wrong. There was real tension in answering the riddle. For taking the risk, we had the dramatic reward of getting past the obstacle, just like the heroes are supposed to do.

This should be used for fairly important riddles, and only when your players have no idea you're going to do it. The riddle should also not be ridiculous, there should be some possible reasonable answers. The more the better, so that when your players pick one and get it right, they feel good about it.

The Hard Core Way

Pick a really hard riddle, and let them suffer the consequences if they can't answer it.

This works best if your players are the sort who won't stress about not being able to answer the riddle, and you are open to creative ways for them to get past the obstacle.

My best example of this is the Order Of The Stick web comic, the episode where the party encountered the classic two men, one of whom always told the truth and the other who always lied. The traditional way of solving this riddle is through logic. The rogue in the party solved it by shooting one of the men in the leg with a hand crossbow. When he exclaimed, "You shot me!", they knew that he was the one who always told the truth.

As a GM you have to be flexible enough to understand your players, and tailor your riddles to what they'll enjoy most. Because, after all, RPGs are all about people having fun playing together.