For a fast-attacker like Nocturne, Fiora or Warwick, I could see starting Krugs to be a good play instead of starting red buff or blue buff. That stun could save you from a lot of pain in early clears.
AtheosisX1 votesYes. Krugs and Gromp are the best starts due to their buffs.
Vore Monster1 votesSmite Krug/Gromp, then get a leash on the buff. You get the smaller camp's buff while getting what you need with reduced damage from the leash.
darkdill1 votesWhy let the smite damage go to waste? Finish Gromp or the Krugs off after you've chunked them. You'll get level 2 as a result.
4nth0l0gy1 votesI still like to get both red and blue first, if possible. It depends almost entirely on the champion, and also where you want to end up after first clear. Some can gank after an entire jungle clear, some need to back after half their jungle and get their Smitem(tm). For example, with yi, I start red, go wolves, get gromp, go blue. I'll either gank top then, or go back and get skirmisher's/stalker's. With Rammus, I'll start blue, get wolves, get red, get krugs, then back.
You can start krugs or gromp for the smite buffs, but I find that they don't really help that much. They don't increase your clear speed dramatically, and they don't deal as much damage as blue or red camp, the first of which you do you will no longer have smite for.
I almost always recommend smiting red buff though; the health gain back is so useful.
TheI3igDaddy1 voteshttp://cloth5.com/exploring-new-jungle-paths/
This article pretty much explains everything. As others have said here, it's better to start on the far ends of the jungle and then complete the closest buff, and depending on how much sustain your jungler has, you either B immediately or you continue on to your second buff.
Heckin Support1 votesStarting grump then blue buff is actually good because you get level 2 off of grump. I'm sure it works the same way for the golems(forget their names already). A new era of jungling is coming.