I haven't done a 24-hour race, or a 100-miler (yet...never say never!) but I have done 12-hour races and 50-milers.
The circuit races I did consisted mostly of a 1km lap that you did over and over and over and over again. You wear a chip and cross a timing mat at every lap. Sounds a bit like a hamster on a wheel, but I enjoyed it. You get a good mix of faster and slower runners, and it is nice to be able to mix with people you generally would not get the chance to. I loved the social side and have made a lot of friends running circuit races. Distance is a great equaliser, I found that a lot of the faster runners slow down a lot at the end of the day.

Mentally you know home-base is right next to the circuit, so there is never that I-am-so-far-from-home-how-am-I-ever-going-to-make-it feeling. You can rest when you want to, although I never take a break of longer than 20 minutes as then I tend to get too stiff. The thing with these circuits is to get a good rhythm going, without going too fast. You have to find that magic pace that you will be able to sustain the whole day.

Other people might differ, but I found it easier to do longer distances on a circuit. You have your safety net and conveniences right next to the circuit. On an ultra you will have to carry what you need (unless there are really good support stations), with a circuit race you just keep everything at your home base next to the circuit.

I set a distance goal for the day. Even though with the races I've done you can stop anytime, once I've reached my goal I usually continue until the time is up.

Training:
If you are planning to do a 24-hour race, I wouldn't skip longer training runs. Maybe for a 12-hour circuit you could, your distance goal depending and if you space your laps well during the day. But, you would still solid 3-hour runs during your training period. A typical marathon training plan could work if you distance goal is 42-50. If more, then you need to train more.

Normally in my build up to longer races I am on marathon running level about 18-24 weeks before my target race. From that point in time I do a marathon as a training run (not race!), 4-6 weeks later a 50k, 4-6 weeks later another 50-56km long run. It is important to space the long training runs. After the last long training run I will do another two high mileage weeks before tapering for 3-4 weeks. During the entire training period we do 3 hour training runs almost every weekend, and/or back-to-back 2/3 hour runs. It is important to be able to run on tired legs. It is fine balance between running enough but not so much that you get injured.

I have been very lucky that I've had experienced long distance runners as training partners who helped me.

I'm currently training for my first 6 hr race. LOL. The options were 6, 12, 24 hrs or 100 miler in 30 hrs or less. I'll be happy with 50k. This race is on a 5k trail loop. Lots of ups & downs, but only 220 ft gain. My intention is to do the 24 hr at Across the Years here in Glendale AZ over New Years 2015. There's many options there, including a 6 day run. Yikes. I'm hoping for 50 miles. Long term, I'm looking at the same race (Across the Years) to do my first 100 miler in Jan 2016. I firmly believe I need lots of miles on these legs in order to cover 100. I currently run about 50 miles per week & I still struggle mentally with the marathon. We have an awesome ultra running community here in Az with Aravaipa Running holding monthly events in the surrounding mountains. I wish I could say that I will run a 100 miler with lots of technical vert, but I may not. The Across the Years race is held on a dirt path that's a little longer than a mile and only slight elevation change. For me, these things take time, mileage, and patience.

I've never been interested in these timed races, because I don't know if I could handle the monotony. When I look at potential ultras, I'm looking mostly at point-to-point courses or loops, since I'm most interested in the experience of travelling through a place. I'll look at some out-and-backs, if it's something like going up a mountain and then back down.

Reading all y'all's replies is making me reconsider. I think a 24-hour run would be a good training run for a 100-mile race.

Guess I'm getting here a little late to the game. Yeah, Zekela and I are doing this 24h thing in just over a week. I still have ankle issues so I may be biting off more than I can chew. But for me the goal is just to keep going. I will be doing a 100 miler in August, and I have never run in the middle of the night, on trails, when my body tells me I should be sleeping...training for the night portion of a 100 mile run is the most daunting aspect for me. I can't exactly go out running in the woods by myself all night. I mean, I COULD, but I'm not afraid to admit that the risk to my safety is more than I am willing to take on.

Though in theory I'm not a fan of loops, the 6.2mi loop will allow me access to my drop bag every 10k, so I won't feel like I need a crew. Logistics are just so much easier with a loop course, which is what these timed races are. I can figure out how I am likely to feel 75 miles into my 100 and plan accordingly when the stakes are higher in a few months. (Do I really want to eat another chocolate covered cherry, Zekela?)

And as I'm slogging along at 3am, I can be inspired by my speedy friend.

For the record, last year runners varied in distance between 12.5 and 106.25.

Kind of on the same train of thought has anyone ever skipped running a full marathon and run a 24-hour ultra or a 50k? Is it a crazy idea? From what I've found it seems like the training is similar for 26.2 as it is for 50k and I'm feeling like a 24-hour race you obviously could set a goal going in that you'd like to complete 50k or somewhere in that range if you'd never run an ultra or a marathon before...

Not crazy at all. I was planning on doing a 50K a couple of month before my full marathon but for some reason North Face decided not to come back to Georgia. I signed up for a 24-hour ultra which will take place one month after my marathon. It's a 5K loop on a trail and I know it's monotonous but several of my running friends will be there and there will be lots of food & good times. I'd like to shoot for 50K and if I feel good I might even go for 50 miles. But I think I'll enjoy the social aspect of it even more.