After playing so many MMOs, especially F2P ones, I've found that any class that can heal themself while also dealing decent damage tends to do the best while soloing. You might not kill monsters as quickly as a pure damage class, but the time/money you save from not having to rest/use potions as much outweighs it. For instance, in the game Fiesta the Cleric was by far the best solo class (and pretty much best class in the game period) because it was the only one that could heal and had great buffs.
That being said, in FFXIV all of the jobs can heal if you get CNJ up to level two before hand. While the cure may be nerfed quite a bit as a DD, it's still great to spam it between fights to get your HP up since you won't be using your MP otherwise. CNJ itself is a great solo class, especially once you do your level 15 class quest and get Aqua Aura. You can start at max range with Stone, Start casting Thunder from THM, then cast Aero as Thunder finishes casting to get both DoTs on the mob at the same time, spam stone/stone II until they get close, then use Aqua Aura to blast them back and root them and finally finish them off with stone spells.
I figured that PUG would be a solid solo choice, but after playing it alongside GLA and CNJ it is pretty weak by itself, at least up to 16 (how long I soloed with it). GLA was the easiest for me to solo with, especially once I obtained some plate armor with high defense. I was always able to do +4 levequests after 15 or so as long as I made sure to only fight one monster at a time. I'm sure MAR would be the same, if not better at this due to it's self healing ability.
I didn't play Archer very long, but it was pretty hilarious how easy it was to solo with. You don't have to actually face the target of your skills so you can simply run around in circles popping off skills and never get touched by melee attacks. Unless they change this I have a feeling Archer would probably be the easiest to solo with so long as you pick your targets carefully.
All in all, every class is built to be good at soloing. Ranged attackers are going to have a notable advantage though, since the majority of monsters use melee attacks exclusively. Tanks will be next on the list with the ability to soak up a lot of damage for constant, sustained fighting. Melee dps will be last on this list, especially PUG, since they don't have as high of defense to absorb hits. Plus from what I've seen most of their moves require positioning for maximum damage that you just won't get very often while solo. They also have a lot of DoTs that won't be very effective against weak targets.
Edited, Jul 22nd 2013 6:27pm by DamienSScott
FFXI: DamienSlvrblade Race: Elvaan Nation: San d'Oria Server: Sylph 2002-2007, Phoenix 2012
PUP WHM PLD MNK BLU BST SAM WAR BLM 99 BRD THF NIN DNC SMN RDM 50+
FFXIV: Damien Scott Race: Duskwight Elezen GC: Limsa Lominsa Server: Ultros
DoW GLA50 ACN50 PUG50 MAR 50 Rest30+
DoH/DoL All 40+