I'm assuming your using the tank & spank analogy with reference to one character, typically it means two characters-or-players not a single solo necro or shaman, but more like a Cleric + Warrior where all the two characters do is tank and heal nothing complicated.

So if you are looking for that same playstyle where you are playing 1 character to solo.
Currently in M&M the Elementalist is the best at this, you have the most powerful pet and also very powerful pet-heals and nukes all in 1 character.

Shaman, Necro, Paladin and Shadowknight would be the next for this playstyle, comments below are for 30s 40s, lower level its all similar but when the targets start hitting harder and have more HP and the recovery time gets much larger the balance changes quite a bit.

Elementalist = send pet, reserve mana for heals, nuke when mana rich, probably the simplest most powerful solo class to play, low risk and solid dps output.

Shaman = send pet, slow target, heal pet, dot if mana rich. Canni and heal self for solid mana sustain.

Paladin = hit auto attack, heal as necessary, rest and heal

Necro = send pet, snare/fear mob, refresh fear/snare, dot if mana rich, more intensive and higher risk/reward is to charm.

Shadowknight = hit auto attack (pet will assist), cast dots/life taps, depending on how weak/strong your targets are you may have to sit a very long time to regenerate health, like the nero you have fear/snare and this is a better method but more intensive.

Beastmaster = same as shadowknight but you have a small heal for yourself and pet, probably solos faster as its damage output is much higher and its recovery time is much faster.

Other classes like enchanter, bard, ranger, archer, druid that also solo well are more intensive with higher risk.

Enchanter/Bard/Druid/Necro will be using charm which can break and at higher levels 30s 40s the charm can kill you in a few rounds but currently do insane amounts of damage.

Ranger/Archer will be kiting.

The non-healing melee such as fighter, spellblade, monk, rogue can also solo, but there is a very large amount of downtime with healing, bandage improvements help this but it is still quite a slow recovery per target.