Well, with cloth, there's no limit, so I'll assume you're asking about disposables.
Personally, while I can't confirm they're the absolute thickest diapers available, the thickest single diaper I've worn was probably an Inspire+ Incontrol Nighttime Briefs by Rearz, which absorbs up to 5L (over a gallon). They're already thick when dry, but swell a lot and get even thicker wet, especially if you soak them with water or have very diluted pee (drink a lot), to take advantage of their maximum absorption capacity.
BetterDrys also come to mind, they swell like crazy, they fit me better than Rearz and are somewhat cheaper. They also have very high leg gathers so you can stuff them with soaker pads and pretty much double the thickness (or more).
Another great diaper is the Bambino Bianco UltraStretch, they're a bit expensive, and perhaps not as thick as Rearz/BetterDrys, but the stretch waist and hook & loop closure system ensure the snuggest possible fit.
I think ABU also makes pretty thick diapers, but I've never tried them.
That said, I also like THICK diapers, so I'll sometimes layer the diapers (poking holes in the inner ones with a fondue fork) and add soakers and/or cloth diapers to the mix, too. In the end, if you're looking for the "forced to waddle like a toddler" kind of thickness, layering and/or soakers and/or cloth are the way to go.