I think it appeals to the three main player types (Timmy, Johnny, Spike) fairly well. It appeals to Timmy because it is a creature that can swing for huge amounts. It appeals to Johnny because of the keeping counters between zones. It appeals to Spike (although Commander is usually casual, I'm sure there are Spikes playing it) because it is aggressive and keeps its advantages (counters) between zones.
I like it as a commander because you can play it early and attack with it, so it is relevant in the early game. Also, so long as you keep on hitting your opponents, it scales nicely with other creatures being played. Later on in the game, it is still a strong commander if it managed to get a few +1/+1 counters on it - it can be somewhat risky with low CMC commanders that they have less of an effect later on in the game, and on the other hand, commanders with really powerful effects usually cost a lot of mana, but this doesn't have those drawbacks.
It also encourages attacking and using it aggressively because, well, if it dies (hopefully trading something), you can get it back and it is the same size (you don't have to start over again). The cheap cost means that playing it from the command zone a few consecutive times isn't going to be greatly prohibitive.
After a bit of planning and searching through gatherer (and my current card collection), I put together a deck (deck list at the bottom of this post).
Here are some of the synergies of some of the card choices I made for the deck.
Rancor, Aspect of Mongoose, Fallen Ideal, Loxodon Warhammer
These are a couple of things to boost the commander (or another creature if needed), that can be reusable. Three of them return to my hand to be re-cast, and the other is a decent equipment that I can re-equip when Skullbriar re-played.
Noxious Revival, Golgari Guildmage, Evolution Charm, Stitch Together, Rise from the Grave
Returning things from my graveyard, to a mixture of my hand/library/battlefield. I sent an email to The Mana Pool recently about Skullbriar as I had concerns about it getting a -1/-1 counter and not being able to play it again as it would die before I could do anything to remove the -1/-1 counter, so I ensured I had a selection to return it to my hand or library to remove the counters if I wanted.
Some static effects that stay around regardless of whether Skullbriar is in play or not.
The most common counter in Magic (I think) is +1/+1 counters, so there are a lot of ways to add these counters, and some other creatures that benefit from them (in the case that I can't put counters on Skullbriar)
Most of the creatures in the deck are associated with +1/+1 counters, and while the first ability might not always trigger as I don't think there are many Warriors, anything with a +1/+1 counter will have trample, which ups the aggression in the deck considerably.
Oran-Rief, the Vastwood
There are more green cards in the deck than black cards, so the effect to put counters on them is relevant a lot of the time. The downside is that it only effects creatures that entered the battlefield this turn, but Skullbriar can enter the battlefield multiple times if it dies, keeping the counters each time, so it is relatively powerful.
Simic Initiate, Aquastrand Spider, Fungal Behemoth, Cytoplast Root-Kin, Soul's Might, Llanowar Reborn
Among other cards, a selection of ways to add counters to creatures.
My favourite combination is casting Soul's Might on a Fungal Behemoth :)
A few creatures that benefit from having counters (there is a lot of putting counters on my creatures, so if Skullbriar is unavailable, these will quite happily have extra counters).
So far I have only managed to play one game since creating the deck, against Liz playing the Kaalia of the Vast pre-made Commander deck (since I got the set of pre-made decks to play with her, this has been her favourite; I don't think I've had a chance to play it myself).
The game was close, I got to play Skullbriar a few times, and it was still relevant as the game progressed, and was slowly adding up some counters. Oran-Rief, the Vastwood was powerful, but did slow me down a little (as I needed to tap it for the effect, I was effectively a turn behind).
In the end I lost against a free Angel, but it was a very close game and, most importantly, a fun game.
This is the current card list, I think there are a few cards I am not too sure on so might replace later on (will have to see what's good in later sets). Doubling Season seems a bit too obvious (and is fairly expensive to buy), but is something I may consider in the future. I haven't included the 'Commander Staples' of Sol Ring (they're all in the pre-made decks at the moment, and a lot of the spells in this deck are colour intensive) and Lightning Greaves (commander already has haste, and I would like to target it to add extra counters).
Some of the effects return cards from the graveyard to my hand or library, while this means Skullbriar will lose its counters, if it has a -1/-1 counter, I would like it to return to my hand or library to re-set it.
Commander: Skullbriar, the Walking Grave
Scute Mob - A cheap creature that can be relevant in the later game
Simic Initiate - A great turn one play to follow with a turn two Skullbriar
Predatory Hunger - When I first started playing Magic, someone lent me a deck with this to play multiplayer with. It was awesome
Rancor - Reusable, powerful
Battlegrowth - Eh, it gives a +1/+1 counter if something needs it
Noxious Revival - Returns something, not great but decent enough
Aquastrand Spider - Early Graft creature, can be helpful as the deck doesn't have a lot of flying
Golgari Guildmage - Efficient. The green ability is great with the commander, the black ability is handy if Skullbriar dies with a -1/-1 counter on it
Bramblewood Paragon - Gives Skullbriar trample (if it has a counter), to help encourage more counters :D
Earthbrawn - Pump in a pinch, or just an extra counter
Evolution Charm - A selection of options, helpful for a Skullbriar -1/-1 counter situation, or to get some more land to play more stuff!
Stitch Together - Some interesting recursion
Demonic Tutor - Go find something awesome
Golgari Signet - Acceleration
Contagion Clasp - Kill opponents creatures, proliferate my +1/+1 counters
Aspect of Mongoose - Reusable enchantment to make Skullbriar harder to kill
Quest for the Gemblades - Add a load of counters to Skullbriar
Shambling Shell - Reusable counter adding
Hunting Moa - More counters
Spike Feeder - Use of counters
Fertilid - This likes having counters of its own, and is a great target for additional counters apart from Skullbriar
Dismember - Excellent removal
Grim Affliction - Removal and increasing my own +1/+1 counter, erm, count
Beast Within - Catch all removal
Putrefy - More removal
Beseech the Queen - Search for stuff (I think I play this in any Black Commander deck)
Cultivate - Efficient acceleration
Mighty Emergence - Once Skullbriar has a few counters, this triggers each time you re-play it
Beastmaster Ascension - Make stuff bigger. It likes the few proliferate spells, and the deck is mainly combat focused
Fallen Ideal - Reusable enchantment, and one of the few ways to deal with flying
Loxodon Warhammer - A powerful card that can be re-equipped when needed
Tumble Magnet - Appreciates the proliferate spells
Dragon Blood - A simple way to continuously add counters
Cytoplast Root-Kin - An awesome card to spread the counter love :D
Fungal Behemoth - Slowly adds counters and then benefits from them
Creakwood Liege - Pumps creatures, and creates some more if needed
Forgotten Ancient - An interesting way to use counters
Fangren Firstborn - The goal of the deck is to attack anyway, I may as well benefit from being so...
Sporeback Troll - More graft
Garruk Wildspeaker - Lots of options with a planeswalker
Hunting Triad - Creatures if needed, or a load of counters
Vigor Mortis - Recursion, with added counter bonus
Vulturous Zombie - Gets counters of its own, and is pretty fun in multiplayer
Spiritmonger - Gets counters, regenerates
Ob Nixilis, the Fallen - Gets counters of its own (there are a few cards that get their own counters, but that doesn't mean they don't appreciate extra ones)
Plaguemaw Beast - Repeatable proliferation
Liliana Vess - Planeswalker abilities can be useful
Incremental Growth - Lots of counters! :D
Soul's Might - Adding a huge chunk of counters if you're lucky. Nice synergy with Fungal Behemoth
Spread the Sickness - Removal AND proliferate? Yes please
Rise from the Grave - Returning stuff
Angelheart Vial - Likes counters, card advantage
Vigor - Gives out many counters
Jugan, the Rising Star - Gives out counters
Simic Basilisk - Graft
Triskelion - Likes extra counters (fun with graft)
Brutalizer Exarch - Utility (the remove-a-problem-non-creature-permanent has been useful when I've played it before)
Contagion Engine - Kill an opponents creatures, multiple, repeatable proliferate. Sweet
Cytospawn Shambler - More graft
Decree of Savagery - Yay counters :D
Protean Hydra - Gets some of its own counters (tempted to replace with the one that doubles its counters that's been previewed in M12...)
Strength of the Tajuru - Addings lots of counters
Profane Command - Handy utility
Command Tower - Mana fixing
Rupture Spire - Mana fixing
Overgrown Tomb - Mana fixing
Llanowar Wastes - Mana fixing
Golgari Rot Farm - Mana fixing
Terramorphic Expanse - Mana fixing
Evolving Wilds - Mana fixing
Vivid Grove - Mana fixing
Llanowar Reborn - Extra counter
Oran-Rief, the Vastwood - Extra counters
Havenwood Battleground - Acceleration if needed
Slippery Karst - Can be useful
Vivid Marsh - Mana fixing
Polluted Mire - Can be useful
14 Forest - Well, kind of essential
8 Swamp - See above