This is, roughly (sometimes you might have to take the commutator subgroup), true if $n$ and/or $q$ are big enough. Wikipedia and sufficiently advanced textbooks on finite group theory spell it out in all the detail.
EDIT: E.g., from the discussion in comments, $SO^+_{2n}(2^k)$ for $n\geq 3$ is not perfect, for it has a simple index 2 subgroup (specified by Dickson invariant).
This is, roughly (sometimes you might have to take the commutator subgroup), true if $n$ and/or $q$ are big enough. Wikipedia and sufficiently advanced textbooks on finite group theory spell it out in all the detail.