The general consensus is that aspirin is good for secondary prevention of fatal heart attacks and strokes, but that it is not for primary prevention. Now there's evidence that cancers might be prevented and treated with aspirin. The decision to use baby aspirin is more compelling now that there's some data supporting that it can not only prevent cancer but also help prevent metastases.
There are two major studies on this. One on 25,000 patients shows a clear benefit to cancer prevention and cancer spread and the other on 100,000 patients shows no significant benefit for the use of aspirin to prevent cancer.
The side effects of aspirin are not infrequent or necessarily minor. For every 73 people treated with baby aspirin, 1 serious bleeding episode such as a retinal bleed, GI bleed, or intracranial bleed occurs. And, it is necessary to treat 162 people for 6 years to prevent one non-fatal heart attack.