Sure! I have only worked with UKC at this point, but there are others out there.
http://www.ukcdogs.com/WebSite.nsf/WebPages/DogWeightPull
The dogs are divided into classes by weight. Placements are given out in each class, although they really don't matter much. The weight classes are 15 lbs apart for smaller dogs and 20 lb increments for big dogs. For example, the Basenjis bascially fall into the 30 lb class. (anything from 16 to 30.9 lbs) There are two ways to calculate placements, and it is decided ahead of time by the clubs holding the event. Format A is by most weight pulled. Format B is by most weight pulled per pound of body weight. It is calculated as a percentage. Most clubs do format A one day and format B the next. Also each day there is an overall winner for both the most weight pulled and most weight pulled per pound for all classes combined. I have seen everything from an American Bulldog to an Italian Greyhound win the most weight pulled per pound. 🙂
All titles in UKC are earned by each dog's individual pulls compared to their own body weight. So classes and placements really don't matter, except for fun. There are 3 types of carts/surfaces to pull with, and each has their own point scale. Snow pulls are the hardest, so it doesn't take as much weight pulled in those events to earn the same amount of points as say a pull with a rail system. Wheeled cart pulls are inbetween, and the rail carts are the easiest to pull. Therefore it takes more weight to earn points. For example, a qualifying score for the first title takes only 3 times the body weight on snow to earn. It takes 7x the weight if its a wheel cart, and then 10x the weight on a rail track. Then to earn championship points after your first title, you only need to pull 5x body weight on snow, but you must pull 10x weight for wheels and 20x weight on rails! The more you pull the more points you earn, up to a max of 20 pts per event. Some titles can be earned by pulling on any of the surfaces. Other titles are for showing off versatility and the dog must earn so many points in two or all 3 of the surfaces to get them. There are 6 titles total you can earn.
IWPA is another organization just for pulling, and they accept all breeds. I have never pulled with them however because the closest pulls in my region are over 3 hours away, up North. We have enough to do with everything else in the dog world that I don't need to make those kind of drives for this. lol
http://www.iwpa.net/
APA is another one I just found this winter doing some googling. They have some pulls very close to home this summer so I am looking forward to going. I don't think they're a very big or influential organization to bother pulling with, at least for Basenjis, but will be nice to check it out.
http://www.weightpull.com/
I think these are all the ones that will accept all breeds. Both IWPA and APA I think give points based on class placements, so I know they have some different formats than UKC.
The only thing you really need is a custom fitted harness. It's an investment of about $50 -100 depending on who you go with and what you make of it. There are 3 harness makers that I've either used or know others personally who have, and they all do nice work and come highly recommended.
Missy Kehler - The Working Canine (she's in the middle of redoing her site)
http://www.theworkingcanine.com/
Harnesses By Carol
http://harnessesbycarol.com/
CD Pits
http://www.itsmysite.com/cdpits/
Most of these sites also have links to training articles, so search thoroughly. 🙂
Our club got to host the "national" snow pull this year for UKC, organized by UNWPA. Here's a link to my little Roxie placing 4th in her class of 8, beating out 4 other Basenjis. This was only two weeks after her very first pulls. (And yes, there's more than one of us crazy Basenji people out here!) And two of those placing Staffies flew out from CA for this! lol Our lovely frigid below freezing MI temps were so welcoming. 🙂 And check out our little racing friend BJ, the IG!
http://www.unitednationalweightpullassociation.com/2009%20shows/UNWPAsnowpull2009.htm
There were several baby goats born at our Ruminant Clinics last days and as I was taking care of them, I saw all the similar behaving as basenjis have. They are same sized, jumping aroud and looking what could they do to have some fun, chewing my shoes and shirt, looking at me like "hey you, what are you doing on my planet?":D, they are just too funny and reminds me basenjis so much 
