Beagles are in some ways very well suited for agility and in other ways they are not. They are fast dogs, built for chasing prey but they tend to be independent thinkers and may not always respond to directions of a handler!
There are some VERY good beagles in agility. One dog, "Joan", has a MACH 13 awarded by the AKC. To get ONE MACH (Master Agility Champion) is a difficult feat and few dogs ever reach that level. Joan has attained 13 of them! There are several other beagles now competing that have obtained one or more MACHs.
Agility is a fast sport in which dogs jump over and climb up obstacles, run through tunnels, and complete weave poles. There are a number of sites dedicated to dog agility and a number of venues for agility trials.
To compete successfully in agility requires teamwork. Your dog and you must work together. Speed and accuracy go hand in hand and a strong relationship with your beagle teammate is very important.
Beagles often want to know "what's in it for me?" Give your beagle a reason to work with you and he will. Food rewards, especially when starting out work very well with beagles in any kind of training, including agility.
Find a good agility instructor and attend classes. PLEASE, keep things POSITIVE! Your dog and you will be learning together. It will take time and patience but with positive reinforcement most people can be successful with their dogs.
For those looking for a good prospective beagle puppy for agility:
In general I would say that the best beagles for agility are those that are outgoing, maybe even a bit on the "snotty" and mischevious side. You want one that is not afraid to try new things, the most adventurous one of the litter. Preferably look for a puppy (and a litter) that the breeder socializes and does various early stimulation activities from a very young age, including introducing noise such as gunshots (gradually building up) to shape the puppies so that they will not develop those fears and will have good sensory stimulation which promotes a good mind from a young age.
If you are truly hopeful to get a good agility beagle, look for a puppy that is very outgoing and inquisitive with little fear. After you bring him home it is, in my opinion, vital to begin teaching good attention skills using a "watch me" command and to continue to give the puppy opportunities to be socialized to a variety of sights, sounds, smells, textures, people, and other well-mannered dogs.
This one is a combination of FAST where points must be accumulated in a 35 second time and a send bonus must be completed from a distance, as well as standard and Jumpers runs. Also seen at: http://www.youtube.com/watch?v=oV5aSsaFER8