- How often did this sort of thing happen?
Not very often, at least not in those numbers. Crucifixion was a common punishment for slaves and lowlifes who committed crimes, but that wouldn't be more than a couple of crucifixions at a time. The usual thing for the Roman army to do would be to sell prisoners of war as slaves - much more profitable than simply killing them. Much of a general's wealth might come from selling prisoners of war into slavery (and I think the troops usually got some kind of bonus too). The only direct reference I can find to a mass crucifixion other than Crassus' is after the Romans defeated the Jewish rebels and captured Jerusalem in 70AD. According to Josephus, the Jewish rebels were displayed around the walls of Jerusalem, rather than being laid out along a road. Rebels were held in pretty much the same regard as criminal slaves - they were a step below even ordinary prisoners of war. It wouldn't surprise me if Romans carried out other mass crucifixions when capturing rebel-held fortresses during other rebellions, but I don't know of any specific reference to that. Mostly when the Romans put down rebellions most rebels didn't live long enough to be crucified - indeed, Pompey also managed to capture around 5000 slaves who escaped Crassus, but he put them to death on the spot.
So the answer to your question is that there is one other documented mass crucifixion, in Jerusalem in 70AD. There may have been more, but it was usually far more profitable to sell prisoners into slavery. And I don't think there's any other instance of a display quite as public as putting the crosses down several hundred miles of highway.
The other reason public displays like this didn't happen after Crassus is that Roman generals weren't concerned about running for election. Crassus was sending a message to his fellow citizens as much as Rome's slaves when he ordered the crucifixions along the Appian way; i.e. 'hey, remember when I saved your asses from those gladiators?'
Crassus was notoriously harsh with his punishments during the Spartacus campaign - he resurrected decimation to punish a legion which had run from Spartacus, which hadn't been used since the early Republic (decimation involved organising in the legion into groups of ten, having them draw lots, and then the other nine beat the loser to death). He was trying to cultivate an image as a tough-guy, no nonsense traditionalist. After the Republic fell, Roman generals didn't really have the need for political grandstanding like that. Even during the Republic there was no real equivalent - Crassus' situation was unique, since there had never been a slave rebellion like Spartacus' before. When most generals won a great battle they would get a triumph in Rome, thereby fulfilling their publicity needs (hence Pompey, who had already had successes in other wars, didn't feel the need to do the same with his prisoners during the Third Servile War). However, Rome was so embarrassed by the whole Spartacus affair that they preferred to forget the whole episode. Crassus chose this particular statement because he knew that the Roman Senate wasn't going to give him a triumph for defeating a bunch of slaves. So those 6000 captured slaves ended up as 6000 billboards along Rome's busiest highway. "Vote for M. Licinius Crassus - no candidate has been more effective at stopping runaway slaves from murdering your family".
- Also did using all the resources for these kinds of display have any impact on the well-being of the legions?
The legions routinely put up and pulled down entire forts while they were on campaign. Every time a legion made camp, thousands of wooden stakes would be hammered into the ground to form a palisade. During the Spartacus campaign Crassus had his legions build a fortification system stretching 40 miles across the toe of Italy (probably a wooden palisade with earth ditches). Putting up a few thousand crosses wouldn't really stretch the legions' logistics much. Also, in Crassus' case he was paying for his legions out of his own pocket, so it didn't even affect the Roman treasury.
Not to criticize the question because it is interesting and I would also like to know the answer but that show also ends by saying that Julius Caesar was killed on March 14th (it was the 15th). It also implies that there is only one consul of Rome (failing to mention there were two at a time). Probably best to not rely on facts drawn from the show.