I'm surprised no one said Warrior >.<
Buffs placed on a Warrior deal and damaging hexes that that trigger due to physical damage is ridiculous... and all that's armour ignoring.
Regarding soloing... there is a very very old thread buried somewhere. The player uses a Warrior and solos a lot of missions/quests using skills from the first campaign. A note for soloing--Hard Mode mobs are going to have there HP raised. This will most nerf certain solo builds simply due to having to burn through a larger amount of HP. I'm thinking Warrior W/N raptors farms and UW SoS farms.
Regarding being useful in a group, all classes do damage in some form. It's not a lot of times where people in PuGs bring skills that taken advantage of physical damage, and that's quite sad: RoJ Monk w/o Strength of Honor? SoS w/o splinter? And those aren't even the overpowered PvE only skills. It seems that although GW is a team game, players just bring the 'best' build for their class and not what may or may not benefit the group. Even so, you get the Fire Ele vs Destroyers :P
A few notes on some of the other classes:
Rits - Most common, SoS: Cast Spirits, twiddle your thumbs. You also get the Soul Twisting variety which is pretty much the same thing. You tend to find like, 5 spirits on each of their bars.
Necros are very versatile - If you're going for team support, you'd probably want to spec in Curses. You'd be able to reduce enemy armour, make them attack slower, and make them attack for less damage; in turn, you'll make your team kill stuff faster while not taking much damage thus making your team kill stuff even faster. You'll have 5 skills open to do what you like.
Assassins - I'm expecting their damage to be nerfed slightly due to coming Hard Mode changes. Most of their damage comes from armour ignoring bonus damage provided by their skills. Still, they do physical damage

Paragons - You'd probably want to wait for some sort of update or you'll find playing P/W _all_ the time isn't very fun.
Rangers - I haven't played around with them too much. I had quite a bit of fun in Normal Mode with them.
Ele's - I got through all campaigns playing as a E/D with a Scythe before the Derv update. If was fun--different, not optimum :P The next update is likely going to make them OP :P
Hope that helped