In Lego BattleBots, different builders make different 'bots, and those bots usually fall into seven main categories.
Vertical bar and disc spinners
Bots of type that have won a championship: 3
These are the most generally successful bot type. Left Hook, a towering windup bar spinner, was the first bot to defeat six-time champion horizontal spinner GyroWave, and its descendant Left Hook Jr. won a total of seven titles. More recently, Skeleton, with a massive weapon powered by thick rubber bands that seem to break every other fight, has split four bots in half (one of them on two occasions) and won three championships.
The highest RPM capability of any vert of this type (or any bot, ever) was that of UpperCut, a bar spinner I made a couple years back. It was fragile and never won a fight, but its bar could probably reach 1200 revolutions per minute (20 per second) and made a terrifying hum. More recently, a similar bot named Divider managed to rack up a single win with its almost equally fast blade, and my superheavyweight Undertaker (pictured) debuted, with even more power than either previous supervert, and though it went winless, its second season ended in the finals, and it defeated three-time champion Skeleton on the way.
Verts are difficult to plan for, since the safest strategy against them is "get under them" which is difficult since verts already want to get under you. This accelerates the fork game, though only flippers tend to take it to crazy lengths.
Vertical drum and eggbeater spinners
Bots of type that have won a championship: None
Drum spinners are the oldest kind of independently powered spinner, and haven't come close to winning a title for years, though they were pretty competitive in early tournaments.
Eggbeaters have largely superseded drums in recent competitions, and though they've never won a tournament, Scrambler, a massive and very durable eggbeater bot, defeated the two-time champion Hydra the second time they met.
Horizontal bar and disc spinners
Bots of type that have won a championship: 4
GyroWave (pictured), the first of this type that *actually worked* still has the record for most championships by a bot, with nine (though three of those were only among my bots, so it doesn't have the overall record). Circle of Death, its hugely destructive successor, fought in ten matches and won nine of them (eight by KO), winning three consecutive championships.
Horizontals are often very effective and damaging competitors, but thanks to Newton's Laws they have one big disadvantage when compared to verticals. When a vert lands a hit, the reaction force pushes it into the floor, and so it stays planted and can deliver a lot of its blade's energy to the opponent. Horizontals, however, not being braced by the ground, are often sent sliding, tumbling, or even flying by their own hits. Also, wedges are very effective at redirecting horizontals' hits and minimizing their deadly attack potency.
Horizontals once dominated the Legobots field, but more recently the meta has turned to the ground game, with weapons like flippers and vertical spinners which need to get under the opponent proliferating.
Horizontal shell spinners
Gigabyte, a real Battlebots shell spinner. (Battlebots Wiki)
Bots of type that have won a championship: None
I've made two of theses, but neither was really any good—it's difficult to make a reasonably light and very strong shell out of Legos. The first one got knocked out of the arena by GyroWave, and the second got beaten up by Fallen Windmill.
Horizontal top spinners
Bots of type that have won a championship: 2
These are just big bladed tops that you spin with your hands. They are usually the most damaging and uncontrollable bots, and their potential for raw, chaotic destruction is unmatched. Son of Razor never won a championship, but it got close (defeating six-time champion Left Hook Jr. twice), Tearnado III surprised everyone by winning back-to-back titles, and more recently Chopper (pictured) has claimed three championships. The greater success of tops in more recent competitions is likely due to changes making it no long possible to knock opponents out of the arena.
The principle advantage of wheel driven horizontals (see above) over top spinners is that they have mass that is not dedicated to the weapon. In addition to not being able to survive if their weapon breaks (the whole thing is the weapon), top spinners almost always throw themselves with an impact, whereas the more conservative horizontals will tend to stay more grounded, or at least waste less of their weapon energy sending themselves flying.
Flippers/launchers
Bots of type that have won a championship: 3
Flippers are less high-energy than spinners, but they transfer the energy with almost 100% efficiency, so while they aren't high-damage competitors, their flips will almost always send opponents higher than an uppercut from a vert.
Haymaker, the first successful flipper, could launch 100 grams about a foot and a half in the air, and Ethan's answer to it, Floppy, which would eventually win three championships, was even more powerful. Eventually I built Hydra, which could launch 100 grams up to three feet up, and 200 grams almost two feet up. It won two titles, and still has the record for the most flips in a match (five to nine—because we didn't count carefully, we'll just say seven).
For all their awesomeness, flippers have one big limitation: they are completely and totally reliant on getting under their opponent. If the other bot has better ground clearance, you're probably screwed.
Hammers and hammersaws
Beta, a real Battlebot. (Battlebots website.)
Bots of type that have won a championship: 1
Hammers are the oldest kind of active weapon in Legobots, and while they usually lack the destructive capability of big spinners, they can still occasionally do serious damage by sniping or jamming weapons and bending frames. However, it's been many tournaments since a hammerbot won the title, and there are currently none on the list of recurring competitors.
Hammersaws are a much rarer and more complex variation of the hammer design, designed for landing more damaging blows. Only one has ever been built, and it went winless, as far as I remember. However, it is absolutely possible for a better-designed one to go deep into the bracket in the future.
Hammers and hammersaws struggle with "hop" which is when the hammer lifts the rest of the bot off the ground—both during the downswing (caused by the hammer's momentum) and at the actual moment of impact (caused by the force transmission). The initial hop decreases control and increases ground clearance, while the impact reaction just wastes energy. (Basically, a hammer is a vertical spinner with a more limited spinup and far less efficient energy transfer.)