No, as long as you are a witch or wizard you don't need a wand to apparate. EDIT:
It has not been directly stated whether or not a wizard needs a wand to Apparate. The requirement of a wand for Apparition remains open to debate.
There are some lines of argument to suggest that a wand is required. During the Infiltration of the Ministry of Magic by Harry, Ron, and Hermione and its disastrous after-effects, Harry thinks about asking Hermione if Mary Cattermole would be able to Side-Along Apparate with her husband Reginald Cattermole without a wand, implying that she cannot. And during the Skirmish at Malfoy Manor, while Harry and Ron are trapped in the Malfoy Manor's cellar and Hermione is being interrogated/tortured by Bellatrix Lestrange, it is directly said that "Ron was now trying to Disapparate without a wand", but was unsuccessful, which leads to the suggestion that Apparating is impossible to do without a wand. However, the impression was given that the manor was charmed, like Hogwarts, in order to prevent any apparating. The only reason Dobby got in and out is because he is a House Elf, they seem to be immune to those particular charms. It is also noticeable that when escaping from Malfoy Manor, Harry made sure to throw a wand at Ron shouting "catch and GO!" before Ron Disapparated. Furthermore, Molly Weasley commented to Fred and George Weasley when they apparated behind her at Grimmauld Place, "Just because you are allowed to use magic now does not mean you have to whip your wands out for everything!", providing further evidence that wands are needed to apparate.
However, there are equally valid counter-arguments that wands are not required for Apparition. At the end of Harry Potter and the Prisoner of Azkaban, after Sirius Black escapes, Cornelius Fudge suggests to Snape that Sirius might have Disapparated. Sirius was currently wandless, and while Apparation is impossible within Hogwarts' grounds, the fact that Fudge sees it as a possibility suggests that Apparition can be completed without a wand. Information about wands supplies further evidence: the channelling of magic to perform a spell or magical ability by holding it in one's hand (This is debatable, during the Dementor attack on Little Whinging in 1995 Harry uses Lumos when searching for his wand in the dark, the wand tip still ignites though he is not holding it. However it is unclear as to if he was touching the wand at the time). Any other method of use -- including mere possession of a wand for Disapparition or Apparition -- is purely conjectural and unsupported by any firm evidence. When Harry wonders whether Mary Cattermole can Side-Along Apparate with her husband without a wand, this is merely a reflection of his lack of experience with Apparition. Evidence confirms that one does not need a wand to Side-Along Apparate (Harry is Side-Along Apparated by Hermione from Bathilda Bagshot's house without a working wand, and Dean Thomas either Apparates or Side-Along Apparates without a wand at all). At Malfoy Manor, the context of Ron's attempt to Disapparate without a wand merely points to his panicked state of mind, since he would not have been able to rescue Hermione, even if he managed to Disapparate without a wand. Malfoy Manor may also have been protected with anti-Apparition spells. So it seems that Apparition can be done without a wand, but is harder to do than it would be with a wand.