There is no definitive list because there is no definitive definition of "system". Sometimes system is synonymous with opening, repertoire, complex, pawn structure, book to sell, etc. What do you mean by system?
What are the main opening "systems"?
I only use a few systems myself and just apply the concepts to all openings It works suprisingly well.
For white I know: For black :
-the mainline Sicilian, -the Najdorf and classic Sicilian,
-London, -slav defense (similar to the London)
Kings gambit
Those are basically the main openings, there is also the ruy lopez, and 4 knights but most people play the sicilian against 1.e4 to avoid all that and so do I! However some people like to play 1.e4 e5 and I play the Italian against stronger players and the kings gambit against the weaker ones.
Realistically you could get away with learning just the London, slav and Sicilian, but I played the Italian since I started playing so i know that also.
That just about covers everything people usually play. Good luck to you!!

The Hedgehog or Hippo are defences that you can play with black without worrying too much about what white plays. The King's Indian Attack and Stonewall are two other white systems. None of these are too popular among GMs, but they are probably playable enough for blitz.

The Hedgehog or Hippo are defences that you can play with black without worrying too much about what white plays. The King's Indian Attack and Stonewall are two other white systems. None of these are too popular among GMs, but they are probably playable enough for blitz.
What I meant by "system" are those openings that you can play against anything regardless of what your opponent plays, rather than specific lines against specific moves. I think riga magician got to what I was talking about.
But why aren't these systems popular? I've been looking over Modern Chess Openings, and it claims that Bobby Fischer used the King's Indian attack a lot. How can it possibly be good enough for Bobby Fischer but not good enough for us regular folk?

For black, try playing a Benko Gambit (aka Volga Gambit), it has some fun potential, and causes white worries.
1.d4 Nf6 2.c4 c5 3.d5 b5 the main line.
Then there is the standard accepted 4.cxb5 a6 5.bxa6 Bxa6.
Or semi declined 4.cxb5 a6 5.e3 Bb7 6.Nc3 axb5 7.Bxb5 Qa5...
Or brew your own declined for the most fun, or accepted for playing into it.
Its a tough opening to face when playing white, the computer has fairly wasted me with it. Black can unleash some surprising and leathal attacks from it.
Another fun opening for black is the Benoni, 1.d4 Nf6 2.c4 c5 3.d5 e6, risky but with attacking potential.
A solid opening for black is the Semi-Slav, 1.d4 d5 2.c4 c6 3.Nf3 Nf6 4.Nc3 e6 5.e3 Nbd7 6.Bd3 dxc4 7.Bxc4 b5 8.Bd3 a6 9.e4 c5 10.e5 cxd4... Play this if you want to have a solid position that is reasonably safe for a while to give you time to develop a strategy.
For white the Kings Indian Attack, 1.Nf3 d5 2.g3 Nf6 3.Bg2 c5 4.0-0 Nc6 5.d3 e6... allows white to develop fairly unhindered, then attack strategicly.
Regular openings for white offer black a lot of choices (king pawn openings), but some can be controlled better by white (some queen pawn openings).
Try the Colle for fun, 1.d4 d5 2.e3 Nf6 3.Nf3 e6 4.Bd3 (important placement) c5 5.b3 Nbd7 6.Bb2 b6 7.0-0 Bb7... for a different take on the queen pawn opening. This opening is also solid, almost like a Semi-Slav reversed.
Just my 2 cents

What I meant by "system" are those openings that you can play against anything regardless of what your opponent plays, rather than specific lines against specific moves. I think riga magician got to what I was talking about.
But why aren't these systems popular? I've been looking over Modern Chess Openings, and it claims that Bobby Fischer used the King's Indian attack a lot. How can it possibly be good enough for Bobby Fischer but not good enough for us regular folk?
He used the KIA a few times, against specific moves by his opponents. Definitely not whatever Black played.
I think they're mostly a myth invented by hack opening book authors.
Of course, you can play the same first x moves against anything, but they're bound not to be the best ones. Good books on "systems" like the Colle point out where you should follow the normal plan, where you shouldn't, where you should do it slightly differently, etc.
Edit: But of course they're close enough to "best" for most amateurs, definitely the < 2000 OTB. I was thinking of the standard that most opening theory is held to.

i use one "system" exclusively for all my chess no matter what side i'm playing :)
it's the kingside fianchetto. this has parts of:
closed sicilian, kings indian attack, kings indian defense, glek (or 4-knights w/ g3), french, pirc/modern...
i basically play the same game everytime ;)
The Leningrad Dutch Defense has system qualities. Against 1. d4 its opening moves can be played against almost any white replies, and the order of moves doesn't matter much. Saves a lot of thought and requires little memory. But its easy to get in trouble with it against the tactically sharp: so I reserve it for playing lower rated players who won't have seen it and whom it will confuse.

Systems, by your definition, are not the best openings available. They help OTB in that you have very few opening surprises but even fewer opening advantages. In addition, there are normally lines which take advantage of "systems" which can lead to a serious disadvantage for the system player if he has not studied his system. Since the main advantage of a system is less need to study this is not unusual.
In CC, systems tend to be worse since there is no suprise or time value. KIA is not bad but there are much better systems against Sicilian, Caro, Pirc, etc.

I think that it is universally agreed that you can not always claim an advantage using systems with the white pieces, or claiming equality with the black pieces. However, the systems you play will be probably more familiar to you than it is to your opponent.
Suppose that you play the Colle, and have played it for many years. Your opponent answer your 1.d4 with ...d5, and let's also assume that your opponent is a guru with 1...d5. You may not be able to claim an advantage, but then you have played the Colle for many, many years, and produced many games. Your opponent on the other hand, hardly ever comes across the Colle, and perhaps he may have prepared for the Colle 10 years ago, I can pretty much assure you that it will be at the very back of his mind whatever he has prepared against the Colle. Of his many years playing 1...d5, perhaps out of every 100 games, only one or two of them will be the Colle, and put into practice what he has prepared.

I understand the reasoning and used it myself back when I played OTB. For CC/online play systems don't work as well. Some systems are better known, more widely used and thus less of a weapon. I believe the Colle fits in here. It seems everyone who plays 1. d4 at some time has used it and it is incredibly popular, with good reason, at club level. If you're tired, or unprepared, its a great one to trot out knowing you won't be smacked in the face with some opening novelty. I would wager that below expert, in the 1. d4 d5 lines you see more Colles, or attempts at such, than QGD's, QGA's, Slavs, etc.
1.... Nf6 is still most popular, which leads to the 2nd system of Trompsky, another thead.
What are the main opening "systems"? I haven't been able to find a definitive list. I know a few, such as the London system and the Colle system. Also, are there any systems for black? They all seem to be for white.
Also, how "bad" are they? From what I've read, they are actually used every once in a while by grandmasters, so they can't be that bad!
Anyway, I've been thinking about adopting a "system" for playing blitz chess when I don't have much time to think about things.