With current technology seems to be the key aspect here. Everyone seems to assume it's just people jumping under their own strength, but what if they have assistance from another object? Like, say, a directed, controlled explosion. I'm pretty sure you know where i'm going from here.
Why explosives? Any other object used to create sufficient force by simply dropping or pushing would have a large mass, which makes the initial movement fairly pointless. Why bother having a double jump if the first jump is 3 inches? Explosives, on the other hand, can generate a HUGE amount of force from a small amount of mass. So what does this mean?
Double Jumps: Yes. Rocket jumps and such provide the additional force directed downwards to result in a 'second' jump. The difficulty comes in controlling the direction, the initial impact itself, the final impact upon landing, and having the resources to do it more than once.
Wall Jumps: Yes. As most people have covered, just look at parkour experts. This becomes a fight of strength against gravity. Pushing off against the wall grants you additional force upwards, although it requires extreme strength to continually move upwards. Likewise, this could be assisted with some form of directed explosives
Directional Reversal: Similar to rocket jumps, direction forces can change your direction, although the effects will be jarring. Imagine jumping straight up in the air and then having a cannon blasted into your stomach. You'll change directions for sure, but it's gonna hurt like crazy. This will have a similar effect. Unlike double jumps, you're going to have to counter your current momentum and some. I suggest armor of some kind.
Once again, these are all fairly dangerous and likely to harm you if you attempt it, other than the wall jumps (which is still dangerous if you're inexperienced). If you want a less dangerous alternative, perhaps try something along the lines of compressed air.