What are some combo heavy Champions?

As I mentioned before, there are different definitions of "combos"

Personally, when I think of "combos" I think of abilities that interact differently depending on the sequence in which they are applied Ryze is a great example of this, when he applies Spell Flux on a target, the effect of his next ability is altered when applied to the same target. Similarly, when Nidalee applies her Hunt mark on a target, her Q and W work differently in cougar form. (Definitions are a bit loose and may be omitting some)

There are people who view "combos" as with a mechanical definition. For example, Riven's "combos" very heavily revolve around her ability to cancel attack animations. This has less to do with the actual order in which she casts her abilities, and more to do with the timing in which she casts her abilities and other attack/move commands. (Notice that a vast majority of these champions have auto attack resets, also same loose definition and possibility of having missed a few applies to this list)

And there are also people who view "combos" as a means to be most efficient in the use of abilities. These are more or less tools for setting up other abilities. Morgana and Lux will prefer to stun an opponent before placing Tormented Soil or attempting to aim Final Spark (which is the actual name for the "Lux Beam" .. interesting how few people actually know that.) This would also include champions who use abilities in a general succession simply because they typically serve as a function of engaging/disengaging for effectiveness. I was honestly going to list every champion who this applies for, ... but to be completely honest, this one includes everyone

probably riven. its more of a button masher once u actually learn which buttons to mash in order

e onto target, q target, then w for a decoy, then r to knock up the enemy or enemies and force them to take the decoy's exploding damage, then, when r is done, e and q onto them again if they survived.

has a lot of different combos.

mannn....

Pre-6 you can W+E+Q and proc thunderlords on them all day @ level 3 from a safe distance..

Post 6 you can R+IGNITE+W (SHADOW BEHIND THEM WHERE THEY WILL RUN)+E+Q...it all happens in an instant..and it shuts them down so fast and hard, then you just R to go back and let your ult proc..

R+D+W+E+Q+R ... I prefer zed though for his heavy poking before 6...then as soon as 6 hits they are either A. Out of health potions. or B. very low on HP...thats when you ult :) happy comboing..

Source: 500k+ exp on zed..mastery 7

...but seriously, when you ult them then shadow behind them so you're infront of them while they retreat..it really kills them, and you can usually hit all 3 shurikens if you're fast enough with it....zed man...Balance is weakness

https://www.youtube.com/watch?v=6NVo5ddBJgM

here you go.. I use it all the time in lane

Honestly, depending on your definition of "combos" ... pretty much every champion in the game is 'combo heavy'. In order to effectively utilize any single champion you pretty much always have to use at least two of their abilities in sequense, and that is by design.

With the considerable exception of many supports. "Allies are low health, .. heal" "Allies are taking damage, ... shield" "Allies need an escape or engage .. cc or buff"

Ryze, Riven, and LeBlanc are the champions with the most versatile set of practically useful ability combos.

etc.