Voicemail that is on your providers end is very reliable.
Normally you can get house..or even business phones for that matter..that have Message Indicator lights, or when you pick up the phone you will hear a stuttered dial tone. (da da da da da) instead of (daaaaaaa). This indicates that you have voicemail. You can call a special number, or dial a three digit code to retrieve your messages.
It can send calls to voicemail when your line is busy, and it can be customized with your own greeting and ring count.
Check with your local phone company for details, but this is how most companies work, Including Verizon, AT&T, and Frontier.
----------------
As regarding Brian's answer- In no way is a phone company's voicemail the Federal Government's responsibility. Each provider has their own voicemail. You can have as many messages as your alloted TIME will allow, not just number of messages. It's your responsibility to see if you have a 10 minute, 30 minute, or 1 hour message time limit before you sign up for voicemail.