I've seen (and had) a lot of questions about professions. So here's a general guide to some of the unique, endgame benefits of actually having certain professions on your character. I will not include, of course, the obvious benefits of being able to craft your own gear / cut your own gems, etc.
Acronyms that should be obvious:
SP - Spell Power
AP - Attack Power
Sta - Stamina
GCD - Global Cooldown
ICD - Internal Cooldown
46 SP, 80 AP or 60 Sta.
Enchanting:
Unique Ring enchants.
46 SP - 2x Enchant Ring - Greater Spellpower,
80 AP - 2x Enchant Ring - Assault or
60 Sta - 2x Enchant Ring - Stamina.
Leatherworking:
Fur Lining for Wrists.
46 SP - Fur Lining - Spell Power vs Enchant Bracer - Superior Spellpower,
80 AP - Fur Lining - Attack Power vs Enchant Bracers - Greater Assault, or
62 Sta - Fur Lining - Stamina vs Enchant Bracers - Major Stamina.
Also various other Fur Linings that can be used for spell resistances.
As well as cost savings in being able to use Jormungar Leg Reinforcements and Nerubian Leg Reinforcements over Frosthide Leg Armor and Icescale Leg Armor, respectively.
Tailoring:
Funky Cloak enchants.
Chance to gain 295 SP for 15 sec (60 sec ICD) - Lightweave Embroidery, or
Chance to gain 400 AP for 15 sec (45 sec ICD) - Swordguard Embroidery, or
Chance to gain 400 Mana - - - - - - (60 sec ICD) - Darkglow Embroidery.
Of course, these cloak enchants have to be compared to the various options from Enchanting and Engineering (see below)
(Usually, 23 Haste, 22 Agi, 225 Armor or 16 Defense Rating enchants are used).
Also Northern Cloth Scavenging (rofl) and Frostweave Net,
as well as cost savings in being able to use Sanctified Spellthread and Master's Spellthread over Brilliant Spellthread and Sapphire Spellthread, respectively.
Inscription:
Powerful Shoulder enchants
46 SP - Either Master's Inscription of the Storm or Master's Inscription of the Crag vs either Greater Inscription of the Storm or Greater Inscription of the Crag,
80 AP - Master's Inscription of the Axe vs Greater Inscription of the Axe, or
40 Dodge Rating - Master's Inscription of the Pinnacle vs Greater Inscription of the Pinnacle.
The above "Greater" shoulder enchants from the Sons of Hodir are purchased for about 100g, this profession should result in some cost savings (depends on how you obtain your Snowfall Ink).
Note: Some tanks prefer the PvP enchant Greater Inscription of the Gladiator due to the benefits of stacking Sta in ICC.
Blacksmithing:
2 extra prismatic sockets
Socket Bracer and Socket Gloves.
E.g. 46 SP from 2x Runed Cardinal Ruby or 60 Sta from 2x Solid Majestic Zircon.
The 2 extra sockets allow you to gain the equivalent of the aforementioned, standard stat increase (46 SP, 60 Sta, 80 AP) by using 2 epic gems. Classes that benefit more from stats other than SP, Sta or AP, such as Strength or Armor Penetration, would see the most use out of Blacksmithing.
Jewelcrafting:
3x Jeweler's Gems
E.g. Rigid Dragon's Eye & Fractured Dragon's Eye
These gems are take up a socket, much like any regular gem, but add more stats than the regular gems. Only 3 can be used, per Jewelcrafter.
In addition to some flexibility in stat gains (see Blacksmithing), the extra benefit from the 3 Jeweler's Gems exceeds the standard benefits from most other professions.
E.g.1 => 3x Runed Dragon's Eye - 3x Runed Cardinal Ruby = 117 SP - 69 SP = 48 SP
E.g.2 => 3x Solid Dragon's Eye - 3x Solid Majestic Zircon = 153 Sta - 90 Sta = 63 Sta
Engineering:
A bunch of unique and cool stuff.
Back - 27 SP or 23 Agi + Parachute
=> Springy Arachnoweave or Flexweave Underlay
Gloves - 340 Haste for 12 sec per min, 885 Armor or damaging rockets every 45 sec
=> Hyperspeed Accelerators, Reticulated Armor Webbing or Hand-Mounted Pyro Rocket
Boots - 24 Crit Rating
=> Nitro Boosts
And that's not all! Engineering has various other funky stuff that can be used for different scenarios, such as grenades & teleporters. This post is already too long for all that (my apologies; please do your own research ).
Of course, these 'tinkers' take the place of regular enchants.
Gathering Professions:
Mining - 60 Sta from Toughness
Skinning - 40 Crit Rating from Master of Anatomy
Herbalism - Healing Cooldown Lifeblood
Alchemy:
1 amazing flask & Mixology!!
47 SP or 80 AP or 40 Str - Flask of the North > Note: This flask is "not consumed when used" i.e. it is effectively a permanent buff as long as you remember to use it.
Mixology - "an increased effect and duration when you drink any elixir or flask you are able to make."
The increased effect for the Endgame Flasks is as follows:
172 SP (125 + 47) when using Flask of the Frost Wyrm
260 AP (180 + 80) when using Flask of Endless Rage
1948 HP (1300 + 648) when using Flask of Stoneblood
63 Mp5 (45 + 18) when using Flask of Pure Mojo
Note: These flasks will last for a total of 2 hours instead of 1 with Mixology, which also increases the effect & duration of 'normal' elixirs such as Elixir of Deadly Strikes.
Also Endless Healing Potion & Endless Mana Potion.
To conclude, I would say that in a very, VERY general, purely endgame PvE context, Melee DPS + Hunters would prefer Blacksmithing + Jewelcrafting, while Caster DPS would prefer Tailoring for optimal stats. In PvP however, Engineering has been shown to shine brighter than the other professions. To each his own however, and like I mentioned at the start, each profession has other benefits that one might prefer (such as the flying carpets from Tailoring <3)
I do hope that this very general guide has been helpful.
Disclaimers:
All numbers and links are from http://wotlk.openwow.com. Do inform me if there are discrepancies with what is 'live'. Openwow isn't 100% accurate but it's the best we've got and it's already pretty good.
This guide is meant to contain information about what each profession has to offer in terms of endgame stats.
Edit: Just wanted to add that the tinkers from Engineering do take the place of regular enchants, just like how the Jeweler's Gems from JC take the place of regular gems.
Edit: Updated the Alchemy section after the fix to Mixology. Many thanks to Nyeriah.
Edit: Hopefully made it easier to read, also added in ICDs for the Tailoring enchants.
Edit: More cosmetic changes. Colours!! ~jazz hands~ (Hope I didn't choose any horrible ones; swapped the bright pink on Tailoring to a softer one in the end.)