If you spend your nights lying awake worrying about having a heart attack, you're entirely justified. But you're probably just making it more likely.
Lars Laugsand et al followed 52,610 Norwegian people for 11 years after the subjects completed an initial survey (investigators can do this in Norway, since they've got everyone's health records in their nefarious socialized-medicine databases).
After adjusting for everything they could (age, sex, marital status, education, shift work, blood pressure, lipids, diabetes mellitus, body mass index, physical activity, smoking, and alcohol consumption), persistent insomnia increased the risk of a first myocardial infarction to the tune of a hazard ratio of 1.45.
These were people reporting difficulty falling asleep almost every night. Since 33% of the population reports insomnia at some point, garden variety insomnia can't be all that bad. However, even those with a feeling of "nonrestorative sleep more than once a week" had an elevated hazard ratio of 1.27 for a first heart attack, compared to those reporting they slept like babies.
Symptoms of insomnia overlap strongly with other psychiatric symptoms of anxiety and depression, which have also been linked to heart disease risk. However, the above associations persisted after controlling for depression and anxiety symptoms (captured by the Hospital Depression and Anxiety Scale in the initial survey).
Clinical Takeaway: Reading this just made you 10% less likely to fall asleep tonight (estimated). Sorry about that.
Laugsand LE et al. Insomnia and the Risk of Acute Myocardial Infarction. A Population Study. Circulation 2011;124:2073-2081.