The question shouldn't be "what are the best professions?", but "what is best suited to my choice of class?".
There are always people who go on about just grinding for money, but it's pretty pointless, as you miss out on the whole point of having a profession for yourself - crafting instead of buying (eg healing potions, weapons, enchants etc).
Engineering is fun, but is most useful for paladins and hunters - Bombs give pulling ability as paladins have no ranged attacks, and of course hunters can make their own guns and ammo. Jumper cables are very useful for a rogue or hunter, since they have an ability to get ooc, although I would never actually rely on them.
Alchemy is probably best for casters, with potions such as +int, +spell attack power, +shadow attack, and of course healing/mana potions. It can be used for any class, but imo it's nothing like as useful. Increased armor potions are also good for a soloing caster as they have such a small amount.
There are +agility potions, and swiftthistle/fadeleaf are used a lot by rogues, so it can be good for a rogue too.
Leatherworking gets very difficult to level as it requires a lot of reagents. There are also very few things at a low level that don't have equivalent/better instance counterparts which aren't too difficult to find. Past level 40(mail), it's pretty useless for a hunter, although there are some nice rogue pieces (stormshroud).
Tailoring (imo mixed with skinning or enchanting is best) should only be taken by casters, as there are some great pieces which are bop. It has value right through to level 60 - giving the first few green pieces, robes of arcana (needed for warlocks), robe of power, then the mooncloth robe/shoulders/head/gloves.
Enchanting with tailoring will give you plenty of green items to disenchant, so it's slightly easier to level. With skinning, you can sell leather to fund buying greens to d/e, although if you're constantly disenchanting the same items, you get a better idea of what you will get (eg brown linen robe gives mostly strange dust).
I've never done blacksmithing, so can't comment on it. I do know that it gets harder at high end when you specialise, as there isn't much that can be made by each "type".