Shuckle is a beastly defensive beast. Its HP is horrible at Base 20 but Base 230 defenses apiece more than make up for it. Depending on EV investment and Nature it can boost one of its Defenses to more than 600 or around 500 apiece. That is higher than any other Pokemon in the game. Not to mention its gets that Sp. Defense boosg from Sandstorm... Shuckle's other stats, however, are horrible. Base 10 in each offense is wimpy at best and Base 5 Speed makes molasses seem fast. However, Shuckle does have two tricks that work perfectly with its poor offensive stats: Power Trick and Power Split. The former requires Trick Room support to pull off successfully, but the latter can be used in any situation. I think Shuckle's bulk enables it to be used in most tiers.
Recommended tiers: NU-OU
Sturdy is the ability to use. When Shuckle has full HP, it will survive an attack that would normally OHKO it with 1 HP. A huge improvement from 4th gen.
Gluttony is totally useless. No one uses pinch berries on Shuckle.
Shuckle is one of the only Pokemon to get Contrary. All of Shuckle's stat boosts become stat drops and vice versa. However, it lacks any moves that can benefit from it. It could be used in Double and Triple battles, but I think Sturdy is still a stronger choice.
Defensive/Supportive Shuckle should not be running offensive moves unless they have Power Split. Most of their damage will come from Toxic. Rest is important for recovery, but unlike most Pokemon Shuckle can usually survive the two turns of Sleep with HP to spare. Encore is a great choice since Shuckle is often used as set-up fodder; locking a foe into a single move is always great. Shuckle can also set up Stealth Rocks (provided its a 4th gen Shuckle), and it has the bulk to set them up multiple times throughout a match. Knock Off can be used as well.
As I said before, Shuckle's trump cards are Power Trick and Power Split. Power Split evenly divides Shuckle's Attack and Sp. Attack with the target, which can be downright crippling to them and usually forces switches. It also beefs up Shuckle's offensive stats by an enormous amount, making attacking viable. Power Trick switches Shuckle's Attack and Defense stats, making it a super-slow Pokemon with incredible Attack, paper-like Defense, and super-high Sp. Defense. It can only be viable in Trick Room.
Shuckle has only a couple of offensive options to use alongside its trumps. It gets the EdgeQuake combo, which is always nice. Gyro Ball works perfectly with Shuckle's snail-like speed. All that's left is Return/Frustration.
I saw an interesting Shuckle set on Youtube that used Rollout, Defense Curl (from 3rd gen tutors), Power Split, and Rest. The Defense Curl/Rollout combo combined with the Attack increases from Power Split allowed Shuckle to pull off some respectable damage. And if it got too weak, it would just Rest.
Double and Triple options: I think multi-Pokemon battles are where Shuckle shines the most. I myself have a Shuckle that uses Power Split and Guard Split. A Pokemon that has shared defenses with Shuckle becomes extremely hard to KO unless Toxic or a Phazing move is used. You can also use Trick Room and Power Trick on the same turn, unlike in Singles.
Countering Shuckle: It's virtually impossible to OHKO a Shuckle with no stat alterations (in fact, I think the only ones who even have a shot are +6 Haxorus, banded Zekrom, and Specs Reshiram). Heck, it's hard to even 3HKO this thing. However, Shuckle does have several disadvantages. It's weak to Stealth Rock, which really cripples its bulk. Its only means of recovery is Rest, and with the new Sleep mechanics in 5th gen, it can end up sleeping for a long time. Finally, it usually can't do much directly to its opponent.
If Power Split or Power Trick are used, however, things get tricky. Since Power Trick only has a shot of working in Trick Room, and Shuckle will be out-slowing everything in it, physical priority moves are your best shot. Bullet Punch, Mach Punch...whatever. Also, since Shuckle needs time to set up, two turns of TR will always be wasted in a Single Battle (one to switch to Shuckle, and the other to set up Power Trick).
Taunt completely ruins all variants of Shuckle. It NEEDS its non-offensive moves to function properly. Without them, it becomes helpless.