This is a topic that gets a fair amount of discussion and has a number arguments on both sides. Let's see what the research and statistics say.
From the Mayo Clinic:
Serious complications associated with chiropractic adjustment are overall rare, but may include:
How common is a stroke after neck manipulation?
This is a difficult question to answer as there are a number of studies that give slightly different statistics.
A few key points to keep in mind.
A study by the Canadian Board Chiropractic Protective board released a report claiming that the rate is 1 in every 5.5 million adjustments while NICMIC (they provide chiropractic malpractice insurance) reported that the rate is no higher than in the general public.
One commonly agreed upon point is that in the extremely rare occurrence that an adjustment may have some involvement in a cardiovascular event there is one particular issue. Extreme rotation of the neck during the manipulation. If someone is already at high risk for vertebral artery dissection extreme rotation may present an issue.
We do not perform any adjustments with this type of rotation and in fact chiropractic schools teach against it with certain contraindications. Things like hypertension, cardiovascular disease, vertigo, dizzyness, blurred vision etc.
At the end of the day the risk of adverse effects is incredibly low and if chiropractic adjustments are performed according to established guidelines is almost non existent.