There might be as many different roulette systems as there are roulette players, but most of those systems are just variations of some common (and ancient) systems. These systems for playing roulette all have one thing in common though; they do not change the house edge or the odds in any way. And no betting progression or system will ever change that mathematical fact.
That being said, no betting system for the game of roulette will reduce your chances of winning either, so there is no real reason not to use one of those systems. The only harm is if you think a system can change you from a losing player to a winning player, because it just doesn't work that way. And no one is well served by being deluded, whether it's a self-delusion or not.
The most common roulette betting system is the Martingale System, and many variations of the Martingale system. The idea is that every time you win a bet, you pocket the bet, but if you lose, you double the size of your previous bet. By doubling the size of your bet, if you win, you'll win back your loss from the previous bet plus one unit. If you lose 2 bets in a row, by doubling your bet again on the 3rd bet, you'll win exactly one unit if you win.
The Martingale System would work great if you had an infinite bankroll and no betting limits. Unfortunately, most (all) people don't play under those conditions. Take a table with a $5 minimum and a $500 maximum bet for example. Using a Martingale progression, you would bet $5, then $10, then $20, $40, $80, $160, $320...then...
Well, at that point, you wouldn't be able to bet $640, and you'd be suffering a pretty big loss that you couldn't recover from. You might be wondering though how likely it is to get 7 losing spins in a row. It actually will happen quite a bit more often than you think it will, maybe once every 90 sequences. And since you're only profiting by one bet every time you hit a win, you won't be up by very much by the time you do hit your inevitable losing streak with the big loss.
Another popular roulette system is the d'Alembert system. This system assumes that after a win, a player is less likely to win again. So after a win, you subtract a chip from your bet. The d'Alembert system also assumes that you'll be less likely to lose after a losing spin, so in that case, you add a chip to your bet. The flaw in this thinking is that the roulette wheel has no memory, and each spin is an independent trial with exactly the same odds of a win or loss as the previous spin.
In a cancellation system you start by writing down a series of numbers. The total of those numbers is the win goal for the session. An easy example would be a session of 1, 1, 1, which is a total of 3. At a $5 table, this would give you a win goal of $15. Each bet you make is the sum of the numbers on each end. (In this case it would be 1+1, or 2.) If you win, you cross off the number on each end, then bets the total of the two remaining numbers.
On the other hand, if you lose, you'll write the number of units you just bet at the end of the sequence, then bet the sum of the two new end numbers. Like the Martingale system above, it doesn't take many losses before the losses become very large, and you hit the maximum betting limit and can't continue, which again guarantees you a loss.
These systems might be fun to try, but they won't change the odds, and they won't magically turn you into a winning roulette player. Betting progressions just don't work that way.