Randonneuring: long-distance, unsupported endurance cycling. This style of riding is non-competitive in nature, and self-sufficiency is paramount.
I have been riding with this group for a little over a year now, the thing I enjoy most is the support from them and encouragement just to keep going. The ride lengths will vary from 100k - 1200k and each rider goes at his/her own pace. Its never a race and there is nothing competitive about it, just a group of folks with a love for cycling. the rides are typically small with groups of 4-20 and most folks ride together, the routes are typically on country roads where the scenery is quite nice and traffic is minimal lending to a great day on the bike. Every route will have controls, a control is a required stop, typically a convenience store where you stop, check in and refuel before going on. The number of controls will vary with the length of the route and are typically 30-40 miles apart. there are time requirements between controls that you have to meet, don't quote me on this but I believe if you average 10mph you will make all controls. Here is an example for a 100k ride, the ride begins at 7am so you must be at the first control of which is at 32 miles by 10:24 and then finish the ride by 1:40pm. None of the rides sponsored by Lone Star Randonneurs have entry fees, so its all free, some rides do require membership in the riding club for liability purposes and i believe annual membership is $25, other rides also require membership in RUSA of which is also $25.
http://www.rusa.org is the parent organization of all United States Randonneur clubs, on this site you will find all the information you care to read.
http://www.lonestarrandon.org is the North Texas group, there is quite a bit of information on their site about local rides and a discussion group. the discussion group is were ad hoc rides are announced such as the Wild Willie 100k posted here.
The group consists of riders at all levels so there is most always someone to ride with, they are also very talented mechanics in the group that you can learn a lot from.
I hope this helps and look forward to seeing you out there, feel free to PM or ask more questions that I have not addressed.