I would say that suicidal thoughts are not unusual but probaly not normal either.
I have been plagued by suicidal thoughts for long periods of my life. At times I have made specific plans and occasionally carried those plans through (unsuccessfully, obviously).
My GP asks me everytime I visit about the frequency and intensity of these thoughts and my motivation to carry them out. We have both come to accept that these thoughts are "normal for me" as part of my depressive illness.
Find someone you can trust, preferably a medical professional who listens properly, and tell them that although you don't have the motivation to carry them through, you are having such thoughts. There are coping techniques and other things a doc should be able to help with. Suicidal ideation can be very intrusive and very disturbing and is best not kept bottled up.