There is no such thing as antigravity, that we know of, if by antigravity you mean some sort of objects gravitationally pushing apart. Early in the universe, there may have been a period of "inflation", where strong repulsive forces pulled the universe as a whole apart, created by a "false vacuum" with a different energy density than the regular vacuum we all know and love. In other words, this effect, which maybe you could call antigravity, would be an effect of space on itself, not an effect between objects in space.
There is some strong indication that the universe's expansion is again speeding up, suggesting that some repulsive effect is at work, but it is not understood yet (the measurements indicating this could even be wrong, but they are gaining support and corroboration).
Tom (and Mike)
p.s. (2009) The evidence that the expansion is accelerating is by now very strong. However, if there's a positive energy density in 'empty' space, that turns out to be the behavior of normal gravity, not some different sort of anti-gravity. Mike W.
(republished on 07/12/06)