Sufficient conditions for the regularity of a context-free language
Every unary context-free language is regular.
(e.g. a direct consequence of Parikh's theorem)
If every iterative/pumping pair of a context-free language L is 
degenerated, then L is regular, i.e. L is regular if, for all words x,u,y,v,z it satisfies:
$$xu^nyv^nz \in L, \text{for all } n \geq 0 \implies xu^iyv^jz \in L, \text{ for all }i,j \geq 0.$$This was proved by Ehrenfeucht, Rozenberg, "Strong iterative pairs and the regularity of context-free languages", 1983. See
"Context-free languages" by Berstel and Boasson for an exposition.
If a context-free language is commutative and linear, then it is regular.
(Ehrenfeucht, Haussler, Rozenberg, "On regularity of Context-free Languages",  1983)