Theoretically there is no limit. Consider a hertzian dipole, this has a constant gain, hence constant effective aperture, but it can be made as small as you like.
As the size shrinks, the bandwidth necessarily shrinks as well (the Q increases), look up a paper by Wheeler "Fundamental limitations of small antennas"
With large antennas (e.g. dishes), it is hard to utilise all the area (and it is usually a complicated tradeoff with spillover), and you can't do better than 1 in this case.
With small antennas, the situation is different, and a well matched, low loss small antenna may well exceed 1.