Through the thousands of years that vampire lore has been handed down, there has never been a definitive set of rules about their powers, nature or limitations. So it only makes sense that with every new author on the topic, their vampires will be both familiar and unique in their traits. The night creatures of The Vampire Diaries are no exception. LJ Smith picked and chose which vampire myths she wanted her characters to be vulnerable to and which she did not, which is the topic of this page: the powers and limitations of VD vampires.

Powers
Basic powers that these vampires may have over their human company: better night vision, greater hearing and sense of smell, all which benefit their lives as hunters. They have incredible strength and speed, along with greater reflexes and other more animalistic characteristics that would allow them to perform feats such as jumping off the roof of a tall building and landing on the ground safely. These vampires possess telepathic powers, which in its weakest form allows them to "feel" the minds of the people around them. A stronger vampire may be able to control the minds of humans and weaker vampires, as well as be able to speak with their minds. The last of its mentioned powers was the ability to shapeshift (turn into animals). Only stronger vampires can shapeshift, and the stronger the vampire the more shapes they can take on. In the novels, Damon was limited two shapes (a wolf and a crow), while Katherine could take on three. Klaus never shifted-shapes during his appearance in The Dark Reunion, so we have no idea how many he was capable of. I can only guess that it was at least four since he was stronger than Katherine. LJ Smith never said whether or not there was an ultimate limit to this ability, so I will assume for the time being that there is none.
In this quartet of novels, the powers of a vampire seem to be obtained only from the amount of human blood they drink. Therefore, the vampire's power can fluctuate month by month (or even day by day) depending on their feeding habits. We see evidence of that when Stefan almost manages (and could have had he not been stopped!) to overtake his brother in the end of book 2 after having just drank the blood of several people, even though he's been living off of the blood of animals for centuries.

Limitations
Like with all power, the super abilities of a vampire do not come without consequences. While they don't cringe at the sight of religious paraphernalia or are deterred by garlic, they are sensitive to the sun. While wearing a special talisman (usually in the form of a ring) set with a lapis lazuli, they can move around in the sunlight without damaging their bodies. However their eyes are still supersensitive to such a strong light source, so direct sunlight can fatigue them and they wear sunglasses on sunny days. Another limitation they are subject to is the need to be invited in (by a human) to any place where humans slept and ate. Stronger vampires are also hindered by running water, as in not being able to cross it. However, neither Stefan or Damon was affected by this limitation, so it's safe to say that you have to be really strong to be affected to this barrier. I think Stefan put it best when he said "The more you belong to the dark, the more the rules of the dark bind you."

Death
In the vampire Diaries, there are two "traditional" and time-proven methods to kill a vampire: a wooden stake through the heart and sunlight without the protection of their talisman. There does appear to be other ways to dispose of these creatures though. In both The Struggle and The Fury, there is evidence that a vampire can die from blood loss. Also in The Struggle, Stefan starts to give a list of methods he calls "more or less effective" which include beheading, burning, driving nails through the temples (ouch!).... So while there are at least 3 definite, effective methods to kill a vampire though there are possibilities for more.