Most powerful WOW character/class for solo-play?

[Artega]

FWIW, I absolutely loved playing my Tauren Shaman.  The reason I picked Tauren over the others was that  I liked the grasslands of the Taurens much better than the nasty red, desert-like scenery of the Orcs and Trolls.  The quest for the fire totem for my Tauren Shaman was rather annoying due to poor directions in the quest log, but that was the only thing I really disliked with my shaman.  It's a very well-rounded class and once you learn how to control the amount of aggro you create, they're quite easy to play.
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Indeed. Tauren Shaman also have a much higher survival capability because of superior Strength and Stamina scores, their racial HP+5% bonus, and War Stomp if you get too many adds for Stoneclaw/Earthbind to take care of. Orcs get a higher Spirit score and a nifty Strength-boosting ability, but I'd still pick a Tauren over an Orc any day.

As for my favorite character, I had a lot of fun with a DPS-oriented Warrior - while I couldn't take as many hits as defensive warriors (because I was using a two-handed axe, and I had zero points in the defensive talents), they can deal out obscene DPS - on the level of Rogues - and because of their Mail (and later Plate) armor, can take more hits than a Rogue ever can. It's a great solo profession if you pick up First Aid and Cooking for secondaries. If you're Tauren, I'd go with Herbalism/Alchemy (+15 Herbalism racial bonus, make your own buff and healing potions, and pawn off extra roots to Enchanters), but otherwise go with the typical Mining/Blacksmithing combo and make some wicked weaponry.

A basic outline of this build:

Deflection - 5 (5% better Parrying)
Cruelty - 5 (5% better chance of Crit)
Improved Charge - 2 (+15 Rage on Charge)
Improved Rend - 3 (+35% bleeding damage)
Deep Wounds - 3 (Free Rend on a crit, essentially)
Improved Overpower - (+50% chance of critting when using Overpower)
Two-Handed Weapon Specialization - 5 (+5% Bonus Damage when using two-handed melee weapons)
Impale - 2 (+20% better criticals - i.e., they do 20% more damage)
Axe Specialization - 5 (+5% chance to crit, for a total of +10% combined with Cruelty - can be swapped for Polearm Specialization, but you'll have to find a place to spend 5 more points in Arms skills)
Sweeping Strikes - 1 (30 Rage 30sec cooldown, essentially Cleave for Battle Stance)
Improved Hamstring - 2 (Increases slow effect by an additional 10%)
Mortal Strike - 1 (30 Rage 6sec cooldown, deals doubled weapon damage and reduces the effectiveness of all healing anything by half for 10 seconds)
Improved Demoralzing Shout - 5 (Increases Power reduction by an additional 25%)
Improved Battle Shout - 5 (Increases Power boost by an additional 25%)
Enrage - 5 (Your next four melee attacks deal an additional 40% damage every time you're the victim of a critical strike)

I was only able to get to LV18 (enough for a Ragefire Chasm run) before the Beta ended, but I had quite a bit of fun with this guy, and he pretty much killed the Felguard in Ragefire by himself (with Priest support, of course - the other three party members were busily running around and drawing adds for us, because apparently the giant Felguard wasn't hard enough.) When WoW is released tomorrow, I'll start him up again and start writing a guide (complete with quest advice) for him, assuming the servers are playable :)