The same technique Allen mentioned also shows that $\mathbb{H}P^{2n}$ doesn't admit any orientation reversing diffeomorphisms.

However, it's also true that $\mathbb{H}P^{2n+1}$ doesn't admit any orientation reversing diffeomorphisms unless n = 0. This is because the first Pontryagin class $p_1 = 2(n-1)x$ for $x\in H^4(\mathbb{H}P^n)$ a generator. Any diffeomorphism must take $p_1$ to itself, so it must take $x$ to itself (unless $n=1$). The ring structure of $\mathbb{H}P^n$ then implies that the diffeomorphism preserves orientation.

(By contrast, the map $[z_0:...:z_n]\rightarrow [\overline{z_0}:...:\overline{z_{n+1}}]$ is an orientation reversing map for $\mathbb{C}P^{2n+1}$).

Another class of (perhaps surprising) examples is exotic spheres: many of them don't admit orientation reversing diffeomorphisms, though, or course, they admit orientation reversing homeomorphisms.

This is because the collection of oriented diffeomorphism classes of an $n$-sphere ($n\neq 4$) form an abelian group under connect sum. The inverse of an oriented diffeomorphism class of sphere is the same diffeomorphism class equipped with the opposite orientation. Thus, exotic spheres with orientation reversing diffeomorphisms correspond to elements of order 1 or 2 in this group.

Then, for example, in dimension 7, the group is isomorphic to $\mathbb{Z}/28\mathbb{Z}$, so there are precisely two spheres which admit orientation reversing diffeomorphisms.