1 high level character
If you raid with a progression guild they'll expect your main character's professions be chosen to maximize raid performance. That's going to rule out most of the better gold making combos unless you're a tank who can take Mining without getting yelled at.
Usually Mining/Herbalism though could also be Mining/Skinning or Herbalism/Skinning. Dual Gathering is best at the beginning of an expansion when raw materials prices are at their highest. Dual Gathering is terrific for leveling toons too, it really speeds up the leveling process and you can either sell the mats to make gold while leveling or save them up to powerlevel a crafting trade once you're 75+. You can't go wrong making every new toon a dual gatherer until you're finished leveling.
Mining + Jewelcrafting
Once you're 75+ this is probably the best low risk gold making single character combo there is. Jewelcrafting/Enchanting can be even more lucrative though it's riskier since you have to depend on others for a source of cheap materials. If you want low risk and easy profits this is the combo to get. And if you're a tank you can even use it for raiding!
JewelCrafting + Enchanting
The most profitable 2 profession combo of all. Riskier than Mining + JC because you're depending on others for cheap ore. If you already have a fair bit of gold and don't mind taking some risk then this is the way to go. A good raiding combo too.
Blacksmithing + Jewelcrafting
Terrific raiding combo and not bad for gold making especially if you're one of the first to get new smithing patterns and can farm or have access to materials only found in heroics and/or raids.
Mining + Blacksmithing
Good combo if you're a high end raider who's likely to be one of the first on the server to get new patterns from new raids. Unfortunately as a high end raider your guild won't let you raid with this combo unless you're a tank. Other gatherer + crafting profession combos fall into the same boat, they're pretty good for gold making if you're one of the first with the new patterns, soso if you aren't. And they might not be good for raiding either.
Other good gold making combinations include Herbalism + Alchemy and Herbalism + Inscription. These combos aren't very good for raiding though.
If you have more than one high level toon (75+) you should seriously consider taking Enchanting on one even if it means dropping another profession you already invested a lot of gold into. Enchanting has a terrific synergy with gear crafting professions because it allows you to make cheap crafted gear and turn them into enchanting materials which you can then either sell as is or after turning them into scrolls.
The Elementium Shuffle (aka Obsidium Shuffle)
The biggest gold maker in the game. Basically you take ore, prospect it, auction some raw gems, cut and sell rare gems, transmute uncommons into rare gems, craft rings, necks and carnelian spikes to disenchant and vendor any excess uncommon gems (mostly zephyrite and maybe some alicite). To do the full shuffle and maximize your profits you need Jewelcrafting, Alchemy (Transmute Spec) and Enchanting. And of course you need a reliable supply of cheap bulk ore.
If you have many high level characters some professions make sense to stack (have on more than one character) while others don't. One profession in particular Alchemy stacks extremely well and Jewelcrafting stacks ok too. From a gold making perspective other professions don't really have any significant advantages to having on more than one character.
Alchemy is generally considered the best profession to stack because you can have three different alchemical specialties on different characters and transmute spec cooldowns are good gold makers. Some players with many high level toons put alchemy on all of them. One potion spec, one elixir spec and the rest all transmute giving them more procs on daily cooldowns like Truegold, Living Elements and probably Epic Gem transmutes in the future.
Jewelcrafting is good profession to stack mainly because it allows you to get more gem cuts sooner than a single character would. JC also has a daily cooldown, Fire Prism, but it isn't nearly as good as Alchemy transmutes.