Balloon Excadrill and Balloon heatran can use EQ locked Dugtrio to set up Swords Dance and Stealth Rock, respectively. Dragonite, Salamence and the Lati Twins can use Choice Locked Earthquakes to set up Dragon Dances and Calm Minds, respectively.
Skarmory walls the set to high hell, as does Forretress. Gliscor, also Walls the crap out of it, and if it isn't the choice Band set, even Blissey / Chansey can toxic stall Dugtrio Out. Tyranitar can come in on any Rock / Dark Attack packed by Dugtrio and throw Ice Beams and Crunches back it, while Jirachi can switch in on all but CB Earthquakes threaten with Body Slam and wish off the damage.
Basically anything with a bit of bulk and a resistance to one of its moves will force it out.
Steelix can come in on any Rock / Dark typed attack and set up Stealth Rocks as can Registeel and also threaten with Seismic Tosses.
Milotic can come in on pretty much any thing and threaten it with Scald. Abomasnow just has to watch out for Stone Edge, but aside from that it can take a couple Earthquakes and threaten with Stab 100% Blizzards.
Same story here, Bulky Waters, steels and anything with a resistance.
Scizor, Lucario, Conkeldurr, Azumarill and anything else with a priority attack can ruin this set. Aside from that, Skarmory can tank Stone Edge and Reversals with little problem, s3t up and then phaze Dugtrio out, rendering Dugtrio completely useless not even being able to switch in again. Gliscor too can Wall it.
Jellicent can take none boosted Stone Edges and use Scald / Will o wisp to shut Dugtrio Down.
Weavile, Mamoswine, Scyther, Toxicroak and Hitmon"X" can all shut it down with Priority. With less walls in UU, resorting to revenging and priority is your best bet at beating it. Toxicroak gets a special mention, as it resists pretty much everything that Dugtrio will pack on this set.
Dugtrio will struggle to get passed Machamp and Ferrothorn / Forretress leads. Scizor being used in lead and Scarfgon being used in lead can U-turn to tyranitar or ... anything and remove of it pretty quickly. Basically, break its sash with a U-turn, switch to something that resists Stone Edge / Earthquake and take it out.
Same Story as above, Scarfed Victini can break its sash with a U turn and switch to Milotic or any random bulky water to get rid of it. Lead Hariyama can get passed Dugtrio fairly easily with the moves Fake out / Close Combat or Close Combat / Bullet Punch.
Token Novelty Set
Skarmory and Gliscor ... and anything with Taunt, like Hydreigon.
Crobat. Will just have to watch out for random Stone Edges. I deeply regret making this set now, but it's a bit of fun