Yes - not necessarily a regular paycheck, but they get financial incentives for good performance.
When Merry and Pippin are captives, the Orcs argue about what to do with them. One Orc from Mordor suggests bringing the hobbits to a winged Nazgul nearby, and another Orc, from Isengard, gets suspicious, and says:
"Maybe! Then you'll fly off with our prisoners, and get all the pay and praise in Lugburz..."
-The Lord of the Rings, The Two Towers, Book III, Chapter 3: "The Uruk-Hai"
"Lugburz" is Barad-Dur, also known as the Dark Tower, also known as the Tower of Sauron - the big black thing with the fiery eye on top in the movies. The implication is obviously that Sauron pays his servants for a job well done.
I have no idea what Orcs would do with the money they earn - the answers to my question about whether there are businesses in Mordor seem to suggest that there is no evidence of any businesses, and outside Mordor, Orcs tend to take whatever they want without paying for it; money is useless if you have nowhere to spend it.
But clearly, this passage makes it plain to see that Orcs do get financial incentives for doing important tasks, and they obviously appreciate these incentives for some reason.
We also learn that, generally speaking, Orcs are fond of objects of value. Just after Sam and Frodo enter Mordor, Frodo has his fateful encounter with Shelob's, and is carried off, unconscious, by Orcs. While trying to rescue his master, Sam overhears two Orc captains, Shagrat and Gorbag, expressing their displeasure with Sauron's regime.
"I’d like to try somewhere where there’s none of ’em ["'em" refers to Shelob, the Nazgul, Sauron, and other "bosses"]. But the war’s on now, and when that’s over things may be easier."
"It’s going well, they say."
"They would. grunted Gorbag. We’ll see. But anyway, if it does go well, there should be a lot more room. What d’you say?-if we get a chance, you and me’ll slip off and set up somewhere on our own with a few trusty lads, somewhere where there’s good loot nice and handy, and no big bosses."
"Ah! said Shagrat, "Like old times."
-The Lord of the Rings, The Two Towers, Book IV, Chapter 10: "The Choices of Master Samwise"
So, left to their own devices, Orcs are inclined to make their living by stealing, looting, plundering, and the like; they also resent being subordinate to other authorities, especially when things go badly for said authorities. Before Shagrat and Gorbag came into Sauron's employ, they used to steal themselves a living, and in their idle moments under Sauron's regime, they dreamed of returning to their old ways, free from the interference of higher authorities. It is also worth noting that these two old friends end up killing each other shortly after this conversation takes place, or at least trying to do so.
It appears that Orcs crave riches, but are inherently prone to infighting and discord. Sauron seems to have taken advantage of these traits by maintaining order through a combination of offering incentives for good conduct and instilling the fear of horrific punishments for those who defy his will.
Note: As Shamshiel points out in his own answer, from an Orc's perspective, being paid too much is not necessarily a good thing, if there are other Orcs around. Orcs tend to use any excuse they can find to kill each other (at one point, an Orc is tired and kills another Orc who won't let him go to bed), so getting lots of nice stuff would probably mean you are going to be murdered and robbed in the very near future.
