Do people without depression ever commit suicide?

Yes. Although major depression and bipolar depression are frequently implicated in suicide, people who are abusing prescription medications or recreational drugs certainly commit suicide also. So do people who are despairing for other reasons - not a full depression, but decision to end life. Panic disorder can also become so anguishing that the person commits suicide as well. These are just a few.
Unfortunately yes. Annual rate of suicide is 12/100, 000 people in the us depression is a condition with many effective treatment options. National suicide prevention lifeline '1-800-273-talk (8255).