Blood Bowl (San Fierro)
The Blood Bowl is located on the southern end of San Fierro. It's similar to a challenge from Vice City, but with a few new twists thrown in.
As you enter the ring, you'll find yourself in a car at the top of a large bowl-shaped depression, along with a dozen or so other cars. Your goal is to get into the large red pillars of light scattered around the bowl, each of which add 15 seconds to your total time; you'll need to reach a minute of time in order to win the challenge. Unfortunately, the other cars in the arena have the same goal, and will thus be heading towards the same pillars as yourself; they'll also be trying to destroy your car, so keep an eye out for wrench pick-ups that will repair your vehicle.
Although the game does keep track of how many vehicles you destroy, it's important to remember that the objective isn't to cause chaos; it's to survive. Since the pillars appear at random, though, part of this is avoiding other cars, while part is just plain luck. If you spot another car heading for a pillar while you're still a distance away, you can pretty much kiss it goodbye. Sometimes, though, the pillars appear fairly high up on the side of the bowl, and the AI cars have a difficult time reaching these.
8-Track (Los Santos)
Although this seems simple - it's a straight-up race against 11 other destruction derby cars - it can actually be somewhat difficult to get through it without burning your car out. You can't take pit stops here, and you don't get any kind of super damage-resistant car, so you'll have to be careful to avoid damage as much as possible, especially in the early race. There's a particular turn that's difficult to make without slamming into the wall, especially when you have a bunch of other cars hassling you, so be careful.
One thing to note is that your car is a bit floaty. If possible, avoid braking; instead, just let up off the gas before turning. Braking, even of the regular variety, will often cause you to spin out. Another item of note is that when your car blows up, you're considered to be wasted, with a full trip to the hospital and the loss of all your weapons that that entails. If you start smoking or flaming, bail out of your car; you'll only be disqualified for this, and will be able to try the race again immediately.
Dirt Track (Las Venturas, Mondays and Wednesdays)
This is another simple race against a bunch of Sanchez-riding maniacs. In terms of pure difficulty, this would be a hard race if it wasn't for the fact that there's a single jump that will usually send all of your AI challengers off their bikes. You'll quickly learn which jump it is, so keep to the inside of the track, avoid the wreckage, take the lead, and keep it. The other racers will crash here each lap, so as long as you avoid any tumbles yourself, you shouldn't have any problems building up an insurmountable lead.
Kickstart (Las Venturas, all days save Mondays and Wednesdays)
Kickstart isn't a race; rather, it's a replica of the motorbike obstacle-course thing we all knew and loved in Vice City. Your objective here is to get 26 or more points while riding around in a Sanchez; green coronas are worth one point, yellow coronas two, and red coronas three. The red and yellow coronas are, obviously enough, going to be more difficult to obtain, but there's one small structure in the center of the ring that's fairly easy to ascend, and will give you around 15 points if you manage to get all of the coronas on it, leaving you plenty of time in which to obtain the remainder of the points that you need. Check the screenshot to see what we're talking about!