Regardless of router security, most website logins and the like use SSL encrypted pages. This is encryption which is client side (on your iphone) If you are unsure if something uses SSL to transmit data you probably shouldn't use it as wackymacky said, anyone can sniff the traffic from your iphone to the router.
Where possible, stick to SSL especially when on unsecure networks. You can never be totally secure but unless you have something someone really wants you'll be fine.