Why do antiferromagnets occur at lower temperature than ferromagnets? The minimal model for describing magnets is the Heisenberg Hamiltonian
$$H = -\frac{1}{2}J\sum_{i,j} \mathbf{S}_i \cdot \mathbf{S}_j$$
Where $i,j$ are nearest neighbors and the factor of $1/2$ is for double counting. 
If $J$ is positive, spins will want to align to save energy (ferromagnets), and if it is negative they will anti-align (antiferromagnets). Ultimately $J$ comes about from Pauli exclusion and electrons not wanting to sit in the same orbital (Coulomb repulsion). 
But if I look at a table of ferromagnets here, I see transition temperatures up to 1400 K. On the other hand, the highest transition temperature for antiferromagnets is a measly 525 K, with most being below room temperature. 
Why do antiferromagnets generally occur at significantly lower temperatures than ferromagnets?
One can argue that maybe $\vert J\vert$ is larger in ferromagnets than antiferromagnets (as one of the current answers does), but this just begs the question. Why should that be the case (assuming it is true)? I don't see an experimentally-verified theoretical basis for asserting $\vert J_{\mathrm{AFM}}\vert < \vert J_{\mathrm{FM}}\vert$. 
This question came up in a class I am teaching to talented senior undergraduates.
 A: It is not correct that AF have low Neel temperatures universally.
One recent popular example is Mn2Au, whose (anticipated) Neel temperature is so high that it can't be reached before the material decomposes. I've heard of estimates in the ballpark of a 1000 K.
There is also the widely commercially applied IrMn, which has Neel Temperatures in the 700-800K ballpark depending on phase and stochiometry and can be probably higher if optimized for Neel temperature.
Other than that, an elemental material can achieve better overall exchange strength with all atoms contributing. As there are no elemental high temperature antiferromagnets, the comparison is slightly unfair. I guess the most fair comparison would be certain phases of CoMn or FeMn alloys, which will probably display Neel temperatures in a similar order of magnitude as elemental Co or Fe.
A: This is just speculation, but the excitation spectrum of a ferromagnet is (in general) quadratic, while the spectrum of an antiferromagnet is linear. Possibly this difference in the transition temperature arises from the greater ease of creating excitations in antiferromagnets.
A: It is the value of the exchange parameter that is smaller for antiferromagnets than for ferromagnets. 
For example,  Iron has $J$ of roughly 0.3 eV and La$_2$CuO$_4$ of 0.13 eV. Iron has a 1000K transition temperature and La$_2$CuO$_4$ of about 325K.
