Q:

How can I tell if a wild animal has rabies?

If I am in the wild and encounter an animal that I think might be rabid, how can I tell if it has rabies?  An animal that has been running hard, or any number of other things could cause it to be foaming at the mouth, but not neccissarily have rabies. Foaming at the mouth is the symptom I most often consider to be a sign of rabies.
The horse in this image, is foaming at the mouth a lot, but I seriously doubt it is rabid 

Related 
How should one properly dispose of a rabid animal carcass? 

A:

In order to understand the question of rabies and whether or not an animal is rabid, a little background information is necessary. 

Once rabies infection occurs, the virus grows in muscle tissue and may go undetected for several days or months. During this incubation (or latent) period, the animal appears healthy and shows no sign of infection.
Usually within 1 to 3 months, the virus migrates to the nerves near the site of the infection and spreads to the spinal cord and brain (i.e., the central nervous system). It usually takes from 12 to 180 days to spread through the peripheral nerves to the central nervous system. At this point, the disease progresses rapidly, and the animal begins to show the classic behavioral signs of rabies. The virus spreads to the saliva, tears, breast milk and urine. The animal usually dies in 4 or 5 days.
Rabies causes typical symptoms. The infection progresses in a predictable manner, from the initial prodormal phase to the excitative, or furious, phase to the final paralytic phase. 
The first sign usually is a change in behavior. Pet owners should be aware that behavioral changes can occur as a result of many conditions, from digestive disorders to poisoning. 
Rabid animals usually stop eating and drinking, and may appear to want to be left alone. After the initial onset of symptoms, the animal may become vicious or begin to show signs of paralysis. Some rabid animals bite at the slightest provocation and others may be somnolent and difficult to arouse. Once the animal shows signs of paralysis, the disease progresses very quickly and the animal dies.
The early symptoms of rabies tend to be subtle, last 2 to 3 days, and include the following: 
•Change in tone of the dog's bark 
•Chewing at the bite site
•Fever
•Loss of appetite
•Subtle changes in behavior
The second phase of infection usually lasts 2 to 4 days and not all rabid animals experience it. Animals that enter immediately into the final paralytic phase are sometimes said to have dumb or paralytic rabies. Animals that spend most of their diseased state in the furious phase are sometimes said to have furious rabies.
An infected dog may viciously attack any moving object, person, or animal; a caged rabid dog will chew the wire, break their teeth, and try to bite a hand moving in front of the cage. Rabid cats will attack suddenly, biting and scratching. Foxes will invade yards and attack dogs, cows, and porcupines.
They may show the following signs: 
•Craving to eat anything, including inedible objects 
•Constant growling and barking
•Dilated pupils
•Disorientation
•Erratic behavior
•Episodes of aggression
•Facial expression showing anxiety and hyperalertness
•Irritability
•No fear of natural enemies (e.g., wild animals may not be afraid of people)
•Restlessness
•Roaming
•Seizures
•Trembling and muscle incoordination
The third and final phase of infection usually lasts for 2 to 4 days. Initial symptoms include the following: 
•Appearance of choking
•Dropping of the lower jaw (in dogs)
•Inability to swallow, leading to drooling and foaming of saliva (i.e., "foaming at the mouth")
•Paralysis of jaw, throat, and chewing muscles
Paralysis then spreads to other parts of the body, the animal becomes depressed, rapidly enters a coma and dies. - Health Communities.

Nota Bene: This also depends on your area. For example the UK has been free of rabies since 1902. Much of Europe is now rabies free as is Australia. So if you do see an animal in these countries that exhibit some of these symptoms it is very unlikely to be rabies – Note added from the comment of Liam.  

A:

From the Humane Society

Nocturnal animals active in the daytime or vice versa.
Excessive drooling
Lack of fear of humans
Aggressive behavior

It does note that there is both a "furious" form where they may act agitated and a "dumb" form where they may act drunk.
From the Merck Veterinary Manual

Paralysis
Seizures
Inability to swallow
Also the type of animal may be an indication, as in some areas, certain species are more likely to have it, with raccoons in the eastern US as an example.

Viewer Discretion is Advised
I found some YouTube videos of rabid animals to more clearly show the symptoms.

Cat
Deer
Raccoon
Another  Raccoon

A:

There are several symptoms that could indicate an animal may have rabies–they have already been shared in other answers to this question–but the only way to know for certain if an animal is actually rabid is to have the brain of the animal examined in a laboratory.
In the past I was CSPS and EMP Level III Advanced first-aid certified. In our training we were instructed that in the event of an animal attack where the animal is suspected of being rabid, we were to make the effort to capture the animal so that it could be tested for rabies. Specifically, we needed to send the head of the animal into the lab so the animals brain could be examined. 
The treatment for rabies is intrusive to say the least. It requires multiple large vaccine injections to the abdomen to help your body identify and fight the virus. I had the process explained to me once by a nurse when I was a child. I had been bit (chewed on) by an animal I caught in a snare and was trying to release. I thought it would give me some sort of outdoors-credibility if I could say I was once bit by an animal and had to get vaccinated for rabies. After hearing about the agonizing process, and the resulting bruising and discomfort, I decided I'd be satisfied with just a scar.

