I think every class can benefit from every Profession in some way.
It virtually comes down to what the player wants on the Character they play...
When you pick a new character, id suggest looking down every avenue for professions, If your going to be a Blade wielding Caster or melee, you might want to take Mining/Blacksmithing, to make your own weapons or armour, dependent on class.
You may want Bombs.. incase your mana runs out, or just for pulling, then again, having the ability to have a chance of rezzing somebody would be good in an instance, so you might want to pick Mining/Engineering
Everyone will, at some point, be needing Potions, whether its health/mana/resistance, every class benefits from atleast one type of potion, at some point.
Every class can also benefit from being a Tailor, well, you can make bags, ofcourse.
Leatherworking can benefit any class except possibly Cloth wearers and Paladins, for a Warrior you could use it to make Ammo pouches, and later on Mail armour (only if your insane and dont want more armour from plate, which is dumb). And then for a hunter/shaman/rogue/druid you could make your own armour