Most policies will have a two year suicide clause that states if the owner of the policy commits suicide within two years of the start of the policy, the policy will not pay out.
And I'm pretty sure if someone has records of multiple suicide attempts prior to trying to buy life insurance, those suicide attempts will probably make the insurance companies to go, "sorry, we ain't gonna cover ya," when the person applies.
Although, like kimopo pointed out, this could all depend on the state.