I personally, and some others, dislike the term symptoms when referring to vampirism as it makes vampirism sound like some kind of disease or illness, which it is not. Some also refer to vampirism as a condition or energy deficiency, but I personally, and some others, frown upon those terms as well, because it gives vampirism a negative connotation.
No one knows nor has been able to determine what causes vampirism. The leading theory is that vampirism may be a combination of genetic, physiological and metaphysical causes. One will often see vampirism referred to as a condition, and then compared to some other physiological conditions such as diabetes or high blood pressure.
I personally prefer to refer to symptoms of vampirism as vampiric traits, characteristics and abilities. However, possessing any or all of these traits, characteristics and abilities does not make one a vampire as many of these same traits, characteristics and abilities can be accounted for by other reasons. All other explanations (i.e., medical, psychological, environmental, etc.) should be explored before assuming that one has those traits due to vampirism.
The key factor in determining if one is a vampire is going to be if one has a genuine need for life-force energies from outside sources and their traits, characteristics and abilities are tied to their vampirism. Also, not all vampires will have all traits, characteristics and abilities. Each individual vampire is different and may have different traits, characteristics and abilities from each other. Just as every individual is different, every vampire is different. Some will have more abilities than others. Some will have more limitations than others.
Physical characteristics:
Pale skin
Sensitivity to sunlight physically (i.e., sunburn easily) and/or visually
Visual sensitivity to any light source
Better night vision than day vision
Eye color changing with mood or for no apparent reason
Heightened senses
Unaccounted-for strength (i.e., stronger than one should be without working out) and quick reflexes
Often feels hungry and/or thirsty despite an adequate food diet
Extreme cravings for certain types of food or extreme cravings that can not be satisfied with food
Often feel run down, fatigued, tired despite an adequate food diet and activity level
Frequent headaches for no apparent reason
Does not require very much sleep
Able to heal quicker than others
Often get sick with "flu-like" symptoms with no medical explanation when they go without feeding for a period of time
Mental characteristics:
Strong-willed; independent nature; confident
Intellectual/highly intelligent
Well-learned/educated, although not necessarily school-educated
Predatory nature
Dark nature
Prefers nighttime over daytime; i.e., nocturnal nature
Moodiness/mood swings/quick-tempered
Mental and/or personality disorders (diagnosed by a medical doctor)
Psychic abilities (although not necessarily psychic feeding methods) and metaphysical characteristics:
Empathy
Telepathy
Mind reading
See and read auras
Extra-sensory perception (ESP)
Clairaudience, being able to mentally hear things from a distance
Clairvoyance, being able to mentally see things from a distance
Clairsentience, having knowledge that one can not explain
Audiovoyance, being able to see and/or hear spirits and possibly communicate with them
Telekinesis
Pyrokinesis
Astral travel/astral projection
Psychometry
Invisibility, although not as in the Invisible Man kind of invisibility; the kind of invisibility where one can blend into a setting, room and/or crowd, and not be noticed by anyone looking for them.
Precognition/visions
Past-life memories, especially vampiric past-life memories
Immortal soul and a belief in reincarnation
Experience déjà vu quite frequently
Able to sense other vampires (often referred to as "vamp radar")
Involved in "alternative" religions (such as pagan, Wiccan, satanic, etc.) or have "alternative" spiritual beliefs
Most are either born vampires or experience an awakening to their vampiric nature later in life, usually in their teen years but it can happen later in life
The above lists are not all-inclusive lists, as I may have missed some characteristics and abilities, but those are the ones that I could think of at this time. These lists of vampire characteristics and traits should not be used as a checklist to determine if one is a vampire.