Han was always planning on paying Jabba back

He was running from Jabba in the originals. It wasn't until the added scene in the rerelease when he agrees to pay him back.
Apparently, Jabba can be reasoned with (Han even talks Jabba down from 20% to 15%), making his scenes in Jedi a lot less powerful.
But CGI

Pidder Padder? Make my Heart go Boom Bap and Then We'll Talk!

It's very likely Star Wars Rebels will surpass the events of Rogue One and IV, and move into the unexplored 3 year region of IV and V. Good that we finally get to see what's going on here and not so good that Disney would be doing it with the "good guys always win" cartoon series.
The Galactic Civil War was basically ignited after the Death Star was destroyed, but for some reason 3 years of the gap between IV and V remain mostly unanswered, even when the expanded universe was in its prime just a few short years ago.

We should one day get a film or TV series set between A New Hope and Empire Strikes Back that could hypothetically further explain why Han never got around to paying Jabba back.
Steve Harris of Iron Maiden is a Brony

I think it's implied from the opening crawl that the Rebels have been on the run since the Imperials destroyed their base very shortly after the first film (and most viewers would interpret TESB takes place a few months later rather than the three years the EU established).

Yes! This. And, what kind of movie ending would we have if he simply paid him back? I don't view it as a plot hole but an aid to keep the plot/trio of Han, Like, and Lea going.

Well, just because the Death Star was destroyed doesn't mean that the whole Empire just surrendered. (Witness the subtitle of Episode V, if you don't believe me.) So perhaps he didn't want to fly all the way back to Tattooine to pay back a giant slug and then get his ship blown out of the sky by an Imperial Star Destroyer.

What makes even less sense is that the Falcon turns into a heap of crap between ANH and TESB. It works fine when he's a smuggler swimming in debt, and jumps to hyperspace without issue.
But then he comes into some money and becomes a senior officer in the Rebel Alliance. He has access to countless astromech and repair droids, every tool in Echo Base, computers, maintenance equipment, and now it won't start unless you punch it. And the big problem that wouldn't allow it to jump to hyperspace BOTH times? Artoo fixes it by turning something.
He couldn't have asked Artoo to look at it in the 3 previous years? WTF?

I seem to remember reading that he was going to but was somehow robbed

And when Han Solo said he had to pay Jabba the Hutt over the bounty, he said it as a goodbye forever, didn't he? Even Leia mentions it later in the film "And then you're gone" . Han Solo wouldn't come back to join the Rebellion after he payed Jabba the Hutt? Anyone find this strange?

Pretty simple answer: Because he's Han.

Not a plot hole at all.
correct, it's a plot point (important difference). It's something that was part of the story. It'd be a plot hole if he paid Jabba back but was still captured by the bounty hunters FOR NO REASON.
"He's dusted, busted and disgusted, but he's ok"

They had just gotten to Hoth when the movie starts. It is stated that the rebellion is being chased around the galaxy by the Empire, Han being with them never had the moment to just leave them high and dry.

My issue is the 3 year gap between ANH and TESB. I always thought it should have been a year between each film (a year passes between TESB and ROTJ, but I would have even preferred 6 months).
Three years makes Han look like an idiot, especially having crossed another bounty hunter, so you'd think he'd make paying Jabba a priority. And it makes Kenobi look like a jerk for letting Luke patrol around on a Tauntaun and do nothing for 3 years, when he could have told him about Yoda a day after Yavin.

I believe Lucas tried to cover this topic with a few lines. At the end of ANH Han is going to pay back Jabba but Luke guilts him into helping and Han helps save the day. Fast forward to Empire and he is still with the Rebellion, he tells general Rieekan that he has to leave to pay back Jabba, Leia runs after him saying she thought Han had decided to say [with the Rebellion] to which Han replies "Well, the bounty hunter we ran into on Ord Mantell changed my mine"
So these things all sum up to Han about to leave to pay his debt but did the right thing and helped in the battle of Yavin, after which he stayed as stated by Leia and then a bounty hunter attacked him on Ord Mantell and we are to assume that it was for his bounty Jabba placed on him that he mentions in ANH. Why Han all of a sudden changed his mind on Hoth im not sure

I agree. It doesn't make sense that he waited so long to pay back Jabba, especially since he had the credits to do so. They're able to jump around the galaxy so quickly in Star Wars that he could have taken a couple of weeks away from the princess to pay his debt.

I have to disagree with you. By paying Jabba back as soon as he had the money, Han would have removed a headache and worry about being killed by bounty hunters. After getting his medal, Han could flown the Millenium Falcon, which can travel at lightspeed, back to Tatooine and pay Jabba the money. Or Han could have sent an emissary. (Do intergalactic wire transfers exist in the Star Wars universe, or is every financial and commercial transaction, including taxation, done by "cash" [i.e. physical currency]?)

Not a plot hole at all. He obviously joined the rebels for a while instead of going back to pay Jabba. Probably he figured they would get close to Tatooine again but they never did. Pretty simple to figure out.