Relating Euler class to other characteristic classes

Question

If I understand correctly, given a complex vector bundle $\pi:E \to X$, its Euler class $e(E)$ is given by $$e(E)=c_k(E)$$ for $k \in \text{min}\{\text{Rank}(E), \text{dim}(X)\}.$

Do we have similar results for other bundles? Say:

1) Real vector bundle?

2) Projective bundle (a fiber bundle whose fibers are projective spaces):

i) Real projective bundle?

ii) Complex projective bundle?

iii) Quaternion projective bundle?

(needed to be oriented.)