While fees vary by provider, and the Department of Labor has yet to turn to fee disclosure of Health Savings Accounts in the same way they do with 401(k)s, you should expect some annual administration fee plus a small percentage of your deposits in the investment portion of your account. Again, check with your provider and if you feel like you are paying too much, by all means speak with your HR department who contracts with these providers on your behalf. And remember, you can always roll your Health Savings Account over to another provider at any point in time (unlike a 401(k) fund where must contribute only to your employer’s selection), but in this case you will need to manage your own tax withholdings.
However, should you leave your employer, your Health Savings Account should be treated as any other account, and I would encourage you to shop around for the best deal possible. It’s a big market and becoming more competitive by the day.