Even if we make them look at the camera,they quickly turn away after a few seconds. Is there any trick to provoke an animal in looking at the camera?
Short answer: No.
Staring is something which indicates hostility and even people will look away if you look at them for more than a couple of seconds. Animals will normally go to great lengths and lots of posturing just to avoid a fight since there's little advantage to being the less damaged animal. To them the camera lens looks like one big unblinking eye.
Anything that considers itself potential prey to you will give you a look to see if you're a predator (and run/walk away accordingly) and may give you a second look over their shoulder to see if you're following. Most predators that consider you prey will do the same if they're not trying to figure out how good you'll taste and if they think they can catch you.
You might get some more interest if you're well camouflaged but it won't be much. Using food/bait/scent of some kind between you and the animal may help get a shot of their face if that's your goal.
The only option is to study the animal(s), learn their behaviour, be ready for the moment and get your timing right to catch that split second when they look back.
A general answer to this will be hard to give. It entirely depends on which species you're looking to capture.
Regarding pets there simply are no general answer. Domestic animals live in a (often) mutual relationship with their owners and both the animal and their carers personality will come into play when you want to make them look into the camera. I'd ask the owner what to do in this situation.
If you're capturing wildlife it depends. Ungulates are easy, especially deer. They have not very good eyesight and as long as the wind is facing you (they can smell you otherwise) and you've found a good hidden spot just whistle. They will immediately stop what they're doing (presumably eating) and stare strait towards you a few seconds and then resume. You can repeat this at least a few times before they even consider retreating.
Birds are a lot harder. They have very good visual perception and will probably have noticed you already and if they still hang around they've considered you not posing a threat and will probably ignore you. You have to wait them out if you want them to look att you. This is less of a problem though since birds have small often black eyes and its hard to tell if they look at you or not. There are exceptions such as owls though.
A general advise to not make the animals feel threatened is to stay inside a car. Somehow it does not pose as a threat to most animals to nearly the same extent as you alone would do.
Provoking wild animals (even to make them turn towards you) is not a good idea, specially at close distances.
If using longer lenses 400mm+ and trying to provoke them by making a noise or throwing stones will just make them alert and they will disappear after a while.
Sometimes, however the animals (in wild) will look towards you if they hear/feel you move or a sound which you make or maybe if your gear is reflecting in the sunlight (not properly camouflaged) - this will again make them realize your presence and move away from you.
There are wildlife photographers who plant remote triggers and cameras to get shots of wild animals (multiple cameras are planted such a way where the animal is moving towards the camera or whole body is visible) but the lucky shots are only a few among hundreds which are captured.
It's again going to be all different for pets, reptiles, birds, cattle, etc.
There is no straight answer for you but your own experience with each species. It's all in the moment and you should be prepared for the shot when it happens.
PS. If you want your wild girlfriend to look towards your cam, just Roar or Wag for that matter.
If you spend enough time watching any animal you can pick up their habits and time your photograph. Most wild animals will regularly look around for predators, and if you are patient you can work out the pattern to it.
For example while birds are feeding or preening, they will regularly look up and around for danger for a few seconds, then resume what they were doing. It's often very regular and predictable. You can not only time a shot where they're looking up, but you can also inch towards them during the times they resume feeding.
I often photograph whitetail deer when I am inside the house and the camera and tripod are outside. I use a wireless remote release. When I first started, I noticed that the sound of the camera itself was enough to get the deer to look up. I set my frame advance rate to Continuous High so that the first shot gets their attention and the second or third gets a head on shot. Here is an example: http://www.flickr.com/photos/chili5558/7327927938/in/set-72157632869717213/lightbox/
As has been stated above, I do not recommend such a technique with dangerous game unless you are willing to sacrifice your DSLR for one good shot.
I have no advice regarding wild animals. But I spent a day with a pet photographer some time ago, and she used a variety of methods. Initially during a sitting, she used different objects to make a short noise, like a squeak, beep, or whistle. This usually made the animal look at her with interest for a moment. She told me that this method only worked briefly, however, as the animal would usually become immune quickly. She then moved on to rattling a jar or can of treats, which again worked for a time (especially if followed with dispensing a treat).
Ultimately, though, she said it's all about learning the animal's body language and gauging the best second in which to take the shot. The only way to really pick up that skill is to spend a lot of time with animals to learn to read the signs. And then take lots of shots.
She was an outstanding pet photographer, by the way.
Try a laser pointer! Depends on the animal, but you can get them to do some pretty interesting stuff with a laser pointer.
Would potentially occupy one of your hands so an assistant/friend might be helpful.
I would always recommend using burst mode when photographing animals - in these days of digital photography memory is cheap and providing you always carry spare memory cards using burst is a great way to go.
I think you have the general bases covered in some of the previous answers - first of all, looking at you is hostile. I would also really wish you don't make noises and throw stones. Imagine someone doing that to get your attention.
Someone also mentioned spending enough time doing photography to understand behavior. That is almost the key here. I try to understand as much as I can about Ecology and Animal Behavior.
Secondly, I do not ever cross the safe distance boundary line, which of course varies both in terms of species and the individual members of a given species. How do you find out where the line is. Stand still or move slowly, and if you get a bit near, then the animal either backs off, flees, or prepares to attack back (which is the last thing you want).
Once you and the species have established the safe distance they will tolerate with you, you can get to work. You should always move as slowly as possible, and for some animals, such as cats or deer, talking in monotone without raising your voice too much might "comfort" them to the point where they are aware of you, and don't think you are going to endanger them imminently. This takes at least a few minutes. Once this is established, usually the animals go back to their routine - cudding their chew, or foraging, and deer in particular will look up from time to time and those create your best moments.
One good rule of thumb is this - are all or the majority of your wildlife encounters fleeting? It means you are not patient enough, and/or are doing things such as your gait, speed, posture and voice that are spooking the animals you encounter. There will always be some fleeting encounters, because they, like us, can simply be moody or shy.
Another rule of mine - I don't use flash with wildlife. It spooks them more than anything else. I understand you sometimes want to, but be aware of the consequences.
Over all, patience, persistence, a good measure of respect for wildlife and species knowledge are your best bets.