Some people make a distinction between the terms "grinding" and "farming." I don't make that distinction. Grinding simply means continuously killing mobs. The goal is to minimize downtime and maximize kills. Whether you are killing for experience, crafting materials, or to make cash, you will want to apply the same basic principals to picking a good grinding spot.
While some classes are more efficient at grinding than others, by following a few basic guidelines, you should be able to pick a spot that suits you.
1. Ease of killing. This will vary between classes and specs. The key idea is to pick mobs that you can kill quickly and without taking too much damage. For low DPS classes, this usually means green con mobs. For casters, this usually means melee-only mobs, which are easy to kite, or simply kill before they reach you. For melee DPS classes without heals, this means mobs with low armor/health, to minimize downtime for recovering health. The best way to find out if the mobs you want to grind meet this requirement for your character is to simply go kill some. See how many you can kill between downtime, whether that means drinking to refill mana, or eating to regain health. A good number to shoot for is 4-5 kills between breaks.
2. Mob Density. The ideal grinding spot will let you continue to kill so long as you can do so. You want to find a spot that lets you quickly move to the next kill without running the risk of unwanted adds coming and ruining your fun. (In fact, if you have movement impairing abilities or spells like Judgement of Justice or Curse of Recklessness that prevent running outright, you should use those while grinding.) Ideal mob density will vary according to your class, and your ability. For AOE grinders, such as Mages or Protection Paladins, very tightly packed groups that are easy to round up en masse are ideal. For slower killers, runners become a problem, so you want a bit more breathing room between mobs.
3. Respawn Rate. You don't want to move between camps of mobs if you can help it, since movement time takes away from killing time. You'll want to find a spot where the mobs respawn at a rate that matches the time it takes you to clear their camp. If you kill fast, you'll want a fast respawn timer, if you kill slow, you want to avoid mobs spawning on you while you're fighting. Mob density and respawn rate are closely related, as they will be determined by your killing rate. This varies highly between individuals, and even over the course of a character's progression, so the best way to find an ideal mix is to experiment.
4. Player Traffic. You want to avoid competition if at all possible while grinding. Even the best grinding areas can only support 2 to 3 players at most and allow for optimal grinding. It's good to have a back up spot to go to if your primary location is busy. The amount of traffic in an area varies greatly by server and by time of day. Also consider teaming up with someone else. This is especially helpful if you're grinding for reputation, less so if you're grinding for experience or to make money. Sometimes a person is in area simply to complete a kill quest, and will welcome the company. By helping someone finish a quest (kill quests are about the most boring type), you might make a friend, as well as get your area back to faster.
5. Type of Mob. If you're grinding for a specific drop (many recipes fall into this category, dropping only off of certain mobs in certain areas), then your choice is made for you. However, if you're grinding for experience, reputation, money, or crafting materials, you can often maximize your efforts by choosing mobs that yield two or more things you need. For example, if you're grinding to level, you'll notice most grinding guides point you toward humanoid type mobs. This is because humanoids drop cash, cloth, and have a higher chance to drop useful (green or blue quality) items. The benefit here is that you get cloth for bandages or for sale. Bandaging is a huge downtime saver, and cloth is always a good choice for the Auction House. Cash is obviously spendable and doesn't take up bag space. Green or blue drops may be used or sold on the Auction House. Here's a short list of mob types and expected drops.
Humanoid: A favorite type to grind on. Drops cash, cloth, higher chance to drop green/blue quality items. The only downside to Humanoids is that their abilities vary greatly, and some humanoid mobs can be too tough to make grinding them worthwhile. Most humanoid mobs run in fear when at low health, which can increase the chance of getting unwanted adds.
Yetis: Yetis are humanoids, but they don't follow the normal rules. Yetis drop cash, but not cloth. Instead, Yetis are skinnable. In addition, Yetis always live in mountainous areas and caves. This makes Yetis the ideal mob to grind for characters that are Miners and Skinners, a great money making combination. They do not flee in fear, which makes the chance of attracting adds lower.
Beasts: Beasts can be skinned, and drop various body parts, which are gray "vendor trash" items. They generally have a lower chance to drop green/blue items (though this is not always true) than humanoids. Most beasts do not run in fear at low health levels. (Plainstriders and some Raptors are two exceptions I can think of offhand.)
Demons: Demons will fall into either the Humanoid or Beast categories above as far as characteristics. Generally, biped demons will have humanoid loot types, and animal types will be skinnable and have animal type loot. Floating heads follow humanoid guidelines. Demons don't flee in fear at low health.
Dragonkin: Dragonkin are essentially like Yetis. They are skinnable but otherwise have humanoid type loot tables. In addition, several types of dragonkin can drop Whelpling vanity pets, which can go for quite a bit on the auction house. (These have an insanely low drop rate, by the way.)
Giants: Generally follow the same rules as Humanoids. Most giants running around are elites, and not closely spaced enough to be worthwhile grinding, even if you're capable of grinding elites at a good pace. Elite dragonkin are always a better choice.
Elementals: Elementals drop cash (even though they have no pockets), have a small chance to drop green/blue quality items, and drop high value vendor trash as well as specific types of crafting supplies that sell on the Auction House for good money. These latter will be either white or green quality items with a name such as Elemental _____ , Essence of ______, or Mote of _______. (The blank will be Earth, Air, Fire or Water depending on the type of elemental.) Which one an elemental drops will depend on the level of the elemental. Currently, Motes, which can be combined into Primals, are the highest value. Rock Elementals in the Badlands are a favorite mob to grind for people saving for their first mount, as the vendor trash value is high, they have good density, don't do high damage, and don't have any particularly annoying attacks to deal with.
6. Location. When picking a grinding spot, you'll want to also have a good location. That means easy access to vendors (to sell trash drops, which add up), a mailbox (to mail salable items to an auction house alt). It's also nice if you're fairly close to the nearest graveyard. Although mobs should be easy to kill, sometimes accidents happen. Another consideration for location is the availability of resource nodes if you have a gathering profession, such as mining or herbalism. Since you'll be in the same spot for an extended period, you'll be able to get in a good amount of gathering if there are a couple of resource node spawns nearby.
