I'm running a prot paladin and holy priest duo. Once you get Judgement of Justice you don't have to worry about runners anymore, and even then I usually let 'em run and bring me more fodder.

As for instances, only some instances can be 2-manned with a tank and healer only. I've only done SM:GY so far, did it at level 32 so I was appropriate level for it, didn't outlevel it yet it still worked. Killing is slower than normal with just a tank and a healer (priest contributing ranged dps on smaller pulls where mana conservation isn't an issue).

The thing about this duo is you can survive *almost* everything. There are some mob types that if you try to AOE tank them down while multiboxing you're in trouble:
* Anything with AOE silence (not only screws up the pally's tanking but prevents the priest from healing)
* Anything with a shield-bash like spell interrupt will constantly interrupt your priest's heals, except renew and power word:shield. Example Hillsbrad Footmen in Hillsbrad Fields, and the Bloodscalp trolls with shields in STV
* Anything with a random-targetted CC ability will probably CC your priest 99% of the time, example Scarlet Scryers in SM:GY liked to put my priest to sleep for 15 seconds. Fortunately, the paladin was tough enough to survive on her own during that time, only once on a 5-pull with two scryers did I have to actually LOH myself *AND* heal myself a few times, because the priest was asleep :P
* Anything that will silence your pally tank will greatly hamper your ability to do damage and maintain threat. Not make it impossible, but just greatly hamper it.

Good times