I've put some thought into this lately figuring out what professions to pick for my alts and then leveling up those professions.
Since WotLK there is much less pressure to get the "right" professions on your toons. Most crafted items are bind on equip so you can send them to whichever alt needs them. Give or take the rewards from each crafting profession are pretty balanced as well. So when you get to 80 it won't really matter.
There is a little more pressure if you are leveling up without the support of a bunch of alts. Blacksmithing on a cloth wearer for example would be perfectly acceptable when it came to the end game to craft gear for your plate wearer, but leveling alone with it would be pretty lame.
So lets take a look at each of the professions and see what it can do for us, who can most benefit from it and how much work is involved in skilling up.
Herbalism - Lifeblood is pretty awesome for leveling once you get your skill high enough to use it. Particularly true for classes that can't heal themselves. That's you mages, rogues, hunters, warriors and warlocks, this could save your life. End game this is less useful than other profession perks, but if you need herbs this is not an option.
The downside is you have to go out of your way to pick up herbs, adding a bit of time to your leveling. With the accelerated leveling through lower level content you spend even more time skilling up instead of leveling since it is easy to move to a new questing area where you find you aren't skilled enough to pick the herbs. Then you have to go back to a lower level area and farm herbs to catch up. This is true of most gathering professions, but herbalism is a little worse due to the fact that skill levels required are much more graduated than say mining. There are many situations where you need to pass up an herb until you get 10 or 15 more skill levels.
Alchemy - You'll have lots of health and mana potions leveling up as well as other utility and buff potions which are fun. Things like water breathing, water walking, invisibility, etc. come in handy in certain situations if your class isn't already capable of such things. There is something for everyone here regardless of class or spec. End game introduces a number of potions with infinite uses (health, mana and a SP/AP flask) which save money and potentially bag space. Other than that you find more herbs (hopefully you or an alt have herbalism trained to a comparable level) and make consumables, endless farming, ew.
Inscription - I've not really got into this yet, but it seems more or less useless for leveling. Basically you make glyphs which you can buy in the auction house for less than the cost of the mats since many of the popular glyphs are made just to train up the skill. You can also make vellum which enchanters love, but again auction house is usually easier. There is a hearth scroll you can make which puts you on par with shamans in how many times you can hearth an hour, but they are consumables. End game there are a number of shoulder inscriptions comparable to the Sons of Hodir reputation rewards, but just a wee bit better to justify the profession. Again you need herbalism to support it, lots of herbing. I'm doing this last basically since I didn't have it on any toon.
Enchanting - Magically disintegrate items into base components and use them to enhance other items. This is another one of those auction house is easier and sometimes better professions, but it has perks. You get the end game bonuses of any other crafting profession in the form of ring enchants. You can disenchant quest rewards and magic items you find to save bag space and level up your profession; no need to go out of your way to farm mats. While leveling you'll probably be enchanting your own gear which you normally wouldn't be if you had to buy those enchants. That is a lot of stats you have leveling you wouldn't normally. Good for any class/spec, you don't have to be a magic savy class to be an enchanter strange as it might be. Downside would be having the extra job of handling shard distribution in groups and any profit from selling disenchantable items goes to your profession instead of your purse while leveling.
I have disenchanting on my rogue and basically leveled her high enough to be able to disenchant any greens I got to make mats to have other enchanters enchant my gear for me. I since took a fancy to my rogue and leveled her high enough to have access to end game enchants herself and can enchant my other toons by using vellum. I paired it up with tailoring (more on that next) which also doesn't require a gathering profession to support it and produced many green items skilling up which I then disenchanted. Any crafting profession is handy for this reason, but all the others need a gathering profession to generate mats.
Tailoring - Useful for cloth wearers leveling up, or to supply cloth wearing alts, or in my case just to make bags (I like to be self sufficient). The main benefit is that you don't need to gather mats aside from just killing stuff normally and looting cloth. That also comes with a disadvantage if you wanted to level up your first aid at the same time as they compete for materials. If I had to do it all over I probably would not of chosen this for a rogue, but end game tailoring has perks that benefit rogues as well so no harm done.
Skinning - Another gathering profession good for anyone interested in taking up leatherworking or making a little money. It would most benefit a melee class or hunter, but only because those are the classes that will need leatherworking mats (arctic furs) for leg enchants later. All classes can benefit from the critical hit chance bonus provided, but casters leg enhancements are made by tailors. Of all the gathering skills skinning doesn't require you to go out of your way, you just skin stuff you kill. Similarly to other gathering professions, due to accelerated leveling you might need to grind your skill up a little from time to time to keep up.
Leatherworking - Useful for leather and mail wearers, or to supply leather or mail wearing alts. That would be hunters, druids, rogues and shamen. Again there is no wrong profession as there are end game perks useful to all classes and specs. End game also has drums to emulate blessing of kings and gift of the wild so non-paladins/druids can share those buffs with their party.
Mining - My least favorite gathering profession, least favorite profession even. I love engineering though so it is a necessarily evil. I wouldn't really recommend it to anyone aside from supporting engineering or blacksmithing. The perk is a stamina buff, which while nice isn't compelling except for perhaps tanks and even then a minor buff (pun very much intended).
Blacksmithing - Useful for mail/plate wearers, or to supply mail/plate wearing alts. That's death knights, paladins and warriors. The main end game perk is additional sockets to put on your gear. Those require gems to be useful though and that costs more money than other profession perks do.
Engineering - My favorite profession because it is fun! There are a lot of toys to play with, some of which are even useful at times. Anyone can benefit from it, hunters especially right now due to ammo alone. The best ammo right now can only be made by engineers, but that could change tomorrow and hunters go back to buying from NPCs. The only downside is the amount to mining you will do to level it up. Another lesser downside is that the engineering enchants aren't perfect for every class/spec. For example the parachute cloak enchant is agility or spellpower and there are classes like death knights that don't really like agility, but it's better than spellpower. Still a small price to pay for a little fun, you can always forgo an engineering enchancement in favor of a more acceptable enchant. Lots of awsome utility type things like portable mailboxes, auction house in dalaran, repair bots, remote bank access, teleporters. No profession comes close to the variety of engineering.
Jewelcrafting - This ranks down there with inscription for me since the auction house is a competitive alternative to this profession. You can make some nicer gems for yourself to gain benefits similar to other professions, but at what cost? There are items to benefit any class/spec though which are handy while leveling if you keep your skill up as you level. End game patterns are bought via jewelcrafting dailies rather than from mats or vendors like other professions.
That's nice, but what professions should I choose?
For new players or new toons without other toons supporting it I'd suggest picking something specific to your armor type. For any cloth wearers that'd be enchanting/tailoring, for leather/mail wearers skinning/leatherworking and for plate wearers mining/blacksmithing.
In general I'd suggest herbalism/alchemy or mining/engineering for everyone and anyone. Those are my two favorites and enchanting/tailoring comes in close behind those two even if you can't make use of cloth items.