What ElvenScribe said, plus gathering alts.
You need 3 gathering alts (ore, wood and herbs), then production alts, as almost everyone is into alchemy and cooking, you need 2 alts there, and if you into any other crafting, thus more alts. (your main probably should do most frequent crafting that you will require, for everything else - there is an alt)
And there are collecting alts, one that you will equip so that it can take mobs 5 or more level higher to collect cards, recipes, production runes, eggs, what-not... Once higher level - move everything and start over.
One thing I forgot to mention, your gatherer will have to be leveled as well and can end up as playable alt, because to gather higher level mats, you have to survive in higher level areas. (and have access to them)
Hope this answers question on how many alts do you really need.