Generally speaking, SAM-e supplements have been shown to be very safe with very few side effects. One reason for the low level of side effects is that SAM-e is a naturally occurring molecule in your body, and a SAM-e supplement simply replenishes your body’s own natural supply. Usually SAM-e side effects occur when you take more SAM-e than necessary. High doses of SAM-e can lead to side effects most commonly mild gastrointestinal upsets (such as nausea, stomach pain, and diarrhea), anxiety, restlessness, headache, and insomnia (usually occurs when SAM-e is taken late at night). When side effects occur you can simply lower your dose or stop taking SAM-e and the side effects should subside. Also see the Sam-e Dosage page for suggestions on how to figure out the best Sam-e dosage for you.
The only side effect that I personally experienced was insomnia. At the time I was taking SAM-e late at night. After doing some research I realized that if I simply changed the time I took SAM-e I would not experience insomnia. I now take SAM-e in the morning and no longer have trouble sleeping.