Yes, depending on your policy, an insurance company can deny your claim. Any denial of a claim must be made on a "reasonable basis." This means that an insurance company must properly investigate the claim and fairly consider the facts revealed by that investigation. But insurance companies do not have to pay every claim. If a claim is debatable or questionable, the company can deny the claim.
However, if an insurance company denies your claim and you believe the claim was denied in bad faith, you should contact an experienced bad-faith attorney to evaluate your case. An insurance company should not look for ways to deny your claim. The insurance company should look for ways to pay your claim. Do not accept the first denial; always ask for a written denial letter listing reasons for the denial.