There are several factors which limit the power an antenna can
handle. For a wire dipole, you can assume a 50 ohm feedpoint and
calculate the current as a function of the power using Ohm's law.
For example, 100 watts results in around 1.4 amps on the wire.
The ARRL handbook has a table of the maximum current carrying
capacity for different wire sizes - I don't have it handy, but use the
value for free air.
Since most wire antennas will have a radiation resistance higher
than 50 ohms, the wire size you calculate for a dipole will be on the
safe side for longwires, quads, etc. The only exceptions would be
some wire yagis and small loops (and other high-Q antennas),
which can have a much lower radiation resistance. These
antennas need larger conductors for reasonable efficiency, and this
will probably limit the use of small wire for these antennas anyway.
The next thing to consider is the voltage gradiant at the ends of
the antenna. The higher the power (and the higher the Q of the
antenna) the higher the voltage at the ends. There are two
conditions to be concerned with. The first is the insulation between
the end of the wire and surrounding conductors. For most antennas
at the 100 watt level, only a small insulator is needed, and, in most
cases, a length of synthetic rope will suffice. But relying on the
wire insulation alone may no be enough. The other condition is
corona discharge from sharp ends ons the antenna - generally this
is not a problem at amateur power levels, but it can happen,
particularly at high altitudes and with sharp ends on a high-Q
antena. The solution is to use rounded ends or plates on the ends
of the elements to spread out the charge.
One remaining possible power limitation is the dielectric strength
of the insulating materials used to build the antenna. I've heard
stories of loading coils wound on PVC pipe which melt at high
power, for example. (This is highly dependent on the additives
in the specific piece of pipe being used.)
You can estimate the voltage across the feedpoint using the
feedpoint impedance and ohm's law. Again, presuming 100 watts
and a 2000 ohm feedpoint impedance (such as a center fed full
wave dipole) this is several hundred volts, which only requires a
small insulator.
Antenna traps containing a capacitor will have a power limit
which is dependent on the voltage rating of the capacitor (and, in
some cases, the maximum current that the capacitor can pass.)
But if you are just interested in experimenting with wire antenas,
and you aren't trying anything fancy, then the truth is that you can
use quite small wire. I've heard of folks running 100 watts into wire
as small as #36, but one problem with wire that small is that the
birds can't see it in time to avoid it, so it often doesn't last long.
(I suspect that #36 is not rated to carry the calculated 1.4 amps,
but it might work on SSB where the duty cycle is very low.)
Somewhere around #28 is a good practical limit for experimenting,
since the wire becomes more difficult to work with if it gets any
smaller.