so far the best I seem to have found (please prove me wrong with statistic, I love numbers) is waiting 5 spins straight where one dozen doesn't come up, then start betting at $1,$2,$3,$4,$6,$9,$14,$21,$31,$47,$70, which covers 11 straight spins straight. I'm only messing around with this, but it's a slow grind, but haven't lost yet.
I know, I know......eventually I'll be prepared to lose my entire bankroll, but that would be only $208.
Please be careful, when I first started out at roulette I tried this system, the time came when I lost and it is painful when that happens... also just trying to win 20 - 30 in a casino and then stopping and moving on won't work either. The time will come when this will catch up with you, and kill you in the first bet. And to lose $208 to win only $1 is really brutal.
The reality is no system can beat roulette.
Best thing to do is get the concept that something is due out of your head, just because something hasn't shown up X amount of times doesn't mean it is going to show, because roulette has no memory.
I tend to bet straight up on numbers at the moment.
One system I use is to just pick a number at random and then stick with it, I don't look for any qualifying criteria. I stop playing when I get bored. This is a really dull way to play, but out of all the systems I've tried this seems to be about the best, keeps your losses low, cause you tend to quit after about 25 misses, and if ladyluck is sitting on your lap, getting plenty of hits on your chosen number at odds of 36/1 is sweet.
Another method I use is to bet on repeating numbers, I choose a number that has hit twice and stick with it. More often than not it will repeat again within 36 spins.
Another method I use is one I call closing the gap, if I see a sequence of numbers like this:
12 5 17 15 36 4
I will bet on number 16 because that is inbetween 15 and 17. You'll be surprised how often that middle number hits, it works as well on live games as on RNGS. But there is nothing to it really, no magic or logic, just freak variance, because some days it won't hit at all.
I sometimes use another system I made up. Where I flatbet. I first chose a random dozen and bet on it for 2 spins, then move to a double street for a further 3 spins, then a single street for a further 6 spins, if it doesn't hit, I then bet on a split for another 6 spins, and finally if I still haven't had a hit, I bet straight up on a number for another 15 spins. Maximum loss of 32 units. Most times I seem to get a hit, but as with all casino games, bad days will happen and you will lose.
Another strategy I use is to play the zero game, which goes against everything I said earlier in the post about the gamblers fallacy, believing something is due after x amount of misses. This system like all others will also lose, but I find it fun to play. What I do is wait for the numbers 0,3,12,15,26,32,35 to have not hit for about 5 - 6 spins, then, place one chip on split 0,3, one chip on split 12,15 one chip on number 26, and one chip on split 32,35. After four misses I put 2 chips on splits 0,3 - 12,15 - 32,35 and leave one chip on number 26. After another 2 misses I ussually stop, or if I'm feeling brave or lucky, I carry on, this time putting 3 chips on the splits and 2 on the number, after a further 2 misses increase to 4 chips on the splits and 2 on the number. Then stop completely. Ussually this works well, as long as you use the rule to quit while your ahead, or the house edge will catch up with you and kick your arse.
I haven't figured out a decent strategy for even bets, best one I've come up with is placing chips on the last one hit flatbetting, but this often ends in a minus.... I don't like progressions much and try to avoid using them, preferring mainly to flatbet.
Best thing to do with roulette if you're going to use systems is to swap and change them throughout the game. Don't keep using the same one, get a feel for the type of game you're playing and then adapt your play to it...
good luck.