Obviously they do, depending on the champion.
First clear is the most important as you are at your weakest, some junglers are low on health after they are done, others can't clear all camps and shouldn't even attempt wolves/krugs and so on.
If you play Hecarim and you start red, you can do wolves right after and it is actually really beneficial to do them as obviously you won't start with machete because you won't lose any health there. In that same situation, if you start red as jarvan, its possible to attempt level 2 cheese gank or do krugs and try to get scuttle after.
Note: as hecarim, you need to be careful to not lose your first/second blue to enemy jungler as your q eats your mana, taking red is fine as long as scuttles are warded, where junglers would obviously path if they want to invade.
Any of these are not 100% what you should be doing every game, as each game is situational based on champions, counters, how lanes are pushed. So you know if you can do scuttle or not.
Most jungle champions have something unique about their pathing you should do about the clear as currently the meta sucks for us junglers. Most of the jungle players just try to gank as much as possible and put pressure in lanes because of the exp nerfs,laners are level 6 when you are 4 so if you don't pull off a gank early on, its not easy to gank a level 6 laner when you don't have ultimate, before it would be very beneficial to just do full clear on many champions, now you shouldn't attempt that in most situations.
When you are lvl 8-9, mid is lvl 11..