Checking a voicemail can be a chore by itself, but to do so only to realise your voicemail icon isn't disappearing afterward is simply frustrating. Often times, your voicemail icon will become "stuck," remaining on the screen in spite of the fact that you have no messages. There are a few things that may be wrong with your phone, and there are simple ways to correct this problem.
Check to see that you have actually heard and saved or deleted all of your voicemails. Dial your voicemail, enter your security code and listen when the recording prompts you. If the recording says you have no new voicemails, your icon is stuck.
Open up your phone's menu. Go to "Messaging," which will most likely contain text and voice messages on current phone models.
Go to "Voicemail." Some phone models have a "Clear Icon" option. If you press this, the icon will disappear whether or not you have messages.
Call your phone from another phone and leave yourself a voicemail if your phone does not have the "Clear Icon" option. Your phone will now really have a voicemail.
Call your voicemail from your own phone and delete the message you left yourself. The icon should disappear now.
Call your the phone manufacturer and/or your phone service provider if none of the above methods work. Something could be wrong with your connection. You may be eligible for a free replacement phone if you are within your phone's warranty.