First, it is known that any irreducible real-valued complex character of the finite general linear group GL(n,Fq), is the character of a real representation. We prove that this is also the case for the groups of symplectic and orthogonal similitudes over Fq, when q is odd. We can use this to find the sums of the degrees of the real-valued characters of these groups, which we also do for the finite orthogonal and special orthogonal groups. Finally, we show that if G is any connected classical group with connected center defined over Fq (q odd), with dimension d and rank r, then the sum of the degrees of all irreducible characters of G(Fq) is bounded above by (q+1)^(d+r)/2, which improves a result of E. Kowalksi.