Sorry if this question has been asked before.
Also, if the Roman army did have units such as this, what sort of training would they have received compared to the normal soldiers?
Well, from what I know and have studied there were no "Roman special forces" that fit our modern idea of special forces; however, there were task forces composed to handle specific duties:
Praetorian Guard were the Emperors elite body guards. They were usually hand picked and Italian born. They actually had a substantial effect on Roman society while they were active due to their organization assassinating Emperors and bringing them to power. More info here: http://www.wenstrom.org/downloads/written/history/rome/praetorian_guard.pdf
There were also select small groups of cavalry and legionaries used to handle specific problems such as civil wars and issues on the Roman frontier, but were later disbanded after the issue was resolved.
R.E. Dupuy and T.N. Dupuy, The Encyclopedia Of Military History: From 3500 B.C. To The Present. (2nd Revised Edition 1986), pp 147-148
Pat Southern and Karen Dixon, The Late Roman Army (1996), chapter 2. ISBN 0-415-22296-6
I have no knowledge of the training needed or given to these units.
If we consider "special forces" to be units designed to cover specific roles then you could say the auxiliary corps as a whole. According to the terrain where they had to operate or the role they were supposed to have on the battlefield, you could find different types of units. There were for example the equites cataphractarii, which were a unit of heavy cavalry supposed to counter their Parthian's counterparts (and later the Sassanids and the steppes tribes). They were introduced by emperor Hadrian. Then there were the sagitarii, which were units of archers (both footed and mounted). During the republic they were usually Cretans, but then the soldiers started coming from other parts of the Empire such as Siria, Anatolia and Thracia (you can see different types of archers on the Trajan Column). The light cavalry can also be considered as a special unit since they could be used as explorers or skirmishers.
I think things were a bit 'looser' than this. So units and legions would be known to be veterans or untested/green troops. Some would be renown for their great deeds, others were either new, or worse, had performed badly. I'd expect them to be given different roles according to their capabilities.
Your question did make me think of the famous capture of Jugurtha (King of a fairly substantial enemy force) by Sulla in 106 BC which, I think, falls into this category.
From memory Plutarch described him taking a small troop of soldiers into enemy territory, negotiating with King Bocchus and then taking Jugurtha prisoner bringing him back to the Roman forces alive, ending the war bloodlessly and marking a crucial point in the Roman influence in Africa.
That's the sort of thing special forces do I guess. As far as I'm aware Sulla had no particular training (quite the reverse, he'd been hanging out with actors for years), or 'special' role in the army, he was just very audacious and made sure he got all the credit.
I think if you want a good answer you need to clarify the question, what do you mean by "special forces"? Furthermore what sort of era are you interested in getting an answer for "Roman" is pretty broad. The Republic or the Empire?
Thanks for all the comments everyone. I appreciate the help.
I have often heard of Julius Caesars Xth legion being somewhat remarkable. However I know little about them specifically. Could somebody, as a follow up question, tell me more about them and if they would be considered special forces or not?
Something interesting to me personally was the Comitatenses. They were created by the emperor Gallienus as a response to the crisis as the "barbarians" were constantly invading the empire during the time. What would happen was there were so many tribes of people invading the empire that by the time the army got to a location and defeated that tribal army, the damage caused would make the citizens in that province no longer trust Rome to protect them. Gallienus solution were the much more mobile, horse-born Comitatenses that could quickly respond to a situation where a much slower response by a legion would take a much longer time to get there.