Edited May 5th, with patch notes.

PvE Rogue: The optimized professions for raids

The choice of professions will be depending on your guild’s needs. If you are the drummer, then engineering and leatherworking are good picks.
If you are not the drummer, engineering/enchanting could be a fair solution until P6 during which you’d replace Enchanting with Jewel crafting (for the neck). Engineering is part of our recommended profession because it brings a solid helm after P2 (goggles) and also an interesting item, the Battle Chicken. In addition, you’ve got Super Sapper Charge alongside various other cool items to use for trash.

On a side note, you can also pick Blacksmithing for Phase 1 in order to craft the Dragonmaw, but past Phase 1 this profession becomes useless. This weapon will be replaced by PVP rewards or raid loots quite easily.

Leatherworking

On The Burning Crusade, Leatherworking offers a lot of useful items both for yourself and your group such as Drums:

Drums of War (+30 attack power and +30 spell damage for your group for 30sec),
Drums of Speed (+15% speed, super useful in certain encounters like Felmyst),
Drums of Restoration,
Drums of Panic,
…and most importantly the famous Drums of Battle (+80 haste)! 

Having those is a prerequisite to apply in certain guilds, but Blizzard revealed that drums meta was a thing to be nerfed, which might affect a bit the guild’s recruitment strategies.

The T6.5 chest Carapace of Sun and Shadow is best in slot and it’s a bind when picked up. That’s why Leatherworking is a great choice for a rogue wishing to be optimal for PvE content.
It also offers nice shoulders to start farming heroics and raids (Switfstrike Shoulders) if you do not have a decent gear part yet (like the Wastewalker Shoulderpads from D3 Wastewalker Set for example)

Engineering

This an interesting profession with good Binds when picked up gear but not best in slot, at least in PvE.
Honorable mention to Quad Deathblow X44 and X11 Goggles. They’re great, but not the best. There is also a great interest for Battle Chicken because they can buff the whole raid with their ability Battle Squawk (5% haste).

Jewelcrafting

This profession will give you unique superior gems; a best in slot neck for both PvP and PvE (Hard Khorium Choker – T6.5, which is part of our Endgame Rogue BiS List as well), a great starter trinket for both PvP and PvE (Figurine – Shadowsong Panther) and a lot of gold. Every player needs gems, don’t forget that.

Enchanting

Considering that you are able to buy every enchants to optimize your gear, the only purpose of the enchanting profession is to add +4 all stats on your rings.
Back in TBC, with both best-in-slot rings enchanted, you would consider dropping it for another profession, but with BC Classic, the profession min-maxing is nerfed and we do not have such an option. Enchanting is a good side option before your main crafting profession but not necessarily an absolute must-have.

PvP Rogue: The optimized professions for Battlegrounds and arenas

The best combination of professions is probably Engineering (X11 Goggles once P2 is out) with Jewelcrafting (Figurine – Shadowsong Panther). Both items also have an endgame upgrade which makes them really interesting through the expansion. These professions also offer numerous good items but they’re mostly relying on these specific items when it comes to PVP optimization.

On a side note, you can also pick Blacksmithing for Phase 1 in order to craft the Dragonmaw, but past Phase 1 this profession becomes useless. This weapon will be replaced by PVP rewards or raid loots quite easily.

Jewelcrafting

In PvP, depending on your gear and your team composition, you will build up agility and/or attack power. Jewelcrafting offers unique gems with improved agility or attack power. 

What is important and the reason why we advise any rogue to pick Jewelcrafting is the trinket! Figurine – Shadowsong Panther increases effective stealth by 1. It may not look like a lot but it makes a huge difference when you combine it with the human racial (Perception). and the engineering head which we will cover shortly… Sbkzor wrote a very informative in-depth stealth guide, make sure to read it if you search for more information on this topic.

Noteworthy is also the endgame T6.5 necklace Hard Khorium Choker. Best-in-slot in PvE, and a really good item for PvP as well.

For these reasons, Jewelcrafting makes a great candidate for a PvP and PvE rogue profession…

Engineering

Oooooh boy, here comes the fun! Engineering is both efficient and extremely fun for PvP. It’s competitive, requires skill, and is very rewarding; particularly when you anticipate where a mage is going to blink at and you throw a grenade at the exact spot!
Anyway, as a rogue, being stealthy is important (duh!) and we saw earlier that Jewelcrafting provides more effective stealth. In a similar vein, Engineering helps you increase stealth detection with Quad Deathblow X44 and X11 Goggles.

With the combination of effective stealth and stealth detection, the rogue dramatically increases the chances he has to have the upper hand during a fight against stealthy characters such as other rogues and druids. It may not look that impressive but those are the most played classes in PvP.
It cannot be stressed enough how important it is for a rogue to have the opener. It’s a game-changer, an enormous pressure on the opponents.
Let’s talk about the other tools that can be handy as a rogue with Engineering:

Frost Grenade (335): Root every enemy in the blast range for 5sec. A pretty great tool against warriors for additional controls.
Fel Iron Bomb (300): Stun every enemy in the blast range for 3sec.
Arcane Bomb (300): Silence every enemy in the blast area for 5sec + drain 50% mana of the damage done.
Dark Iron Bomb (285): Stun every enemy in the blast range for 4sec.
Parachute cloak (225): Reduces the fall speed for 10sec. Combined with the next gadget and you have a fun way to fly in Alterac or across Warsong!
Rocket Boots Xtreme: +300% speed for 3sec. When faded, deals a bit of damage that can be used to break a cc like a polymorph, blind, gouge, or anything else that breaks on damage. To be used for fun or to break an anticipated cc. [warning: cannot be used in arenas in 2.4.3]
Gnomish Cloaking Device: Invisibility for 10sec (not stealth, IN-VI-SI-BI-LI-TY!). A great and dramatic escape … with 1h CD.
Goblin Land Mine: To be placed around a flag or a capture point to spot stealth enemies.

Gnomish Engineering:

Gnomish Poultryizer (340): Turns the target into a chicken for 15sec. This is my favorite toy in the game. A silence of FIFTEEN SECONDS! FIFTEEN!
Nigh Invulnerability belt (350): Absorbs 4000 damages for 8sec. This fails around 15% of the time and… doubles the damage taken from all sources. Extremely popular in arenas during Season 1
Gnomish Flame Turret (325): Quickly constructs a gnomish flame turret at your feet that will nearly always attack nearby enemies. It’s so fun to use that to mess with enemies trying to cap a flag. It does cost a lot given its inefficiency but IT’S FUN.
Gnomish Alarm-O-Bot (265): Summons an Alarm-O-Bot for 2 minutes that occasionally sends out a pulse that detects nearby stealthy or invisible enemies. This one is also so fun in battlegrounds. How often do you see one of those there? Not very often, I guess. ORIGINAL CONTENT! Make them laugh and then kill them mercilessly.

Goblin Engineering:

The Big One (235): Inflicts 340 to 460 Fire damage and incapacitates targets for 5 seconds in a 10-yard radius. TEN YARD RADIUS, FIVE SECONDS STUN. You couldn’t miss your target even if you were blind.
Super Sapper Charge (340): Explodes when triggered dealing 900 to 1500 Fire damage to all enemies nearby and 675 to 1125 damage to you. This is an absolute must-have to duel rogues and break their vanish.
Goblin Sapper Charge (205): Super Sapper Charge’s little brother. Less damage but same purpose. Costs less to make..
Goblin Rocket Boots (225): A sprint of 20sec with 30% chance of failure. Meh. 5 Min CD Cool! If they malfunction, they’re destroyed… Just go for the gnome version. Basically, Goblin boots are faster with shorter cooldown, Gnomish boots are safer with longer cooldown.