VoIP "can" work over dial-up with only 56Kbps speed.
Keeping in mind that VoIP over dial-up is best used as a Long Distance calling alternative and not as a Home Phone option.
You can only call from your PC with headset and microphone.
To successfully use VoIP over Dial-up Internet you are restricted to VSP's (Voip Service Providers) that default to or allow you to set your acount for "Low Bandwidth Codec". Most traditional VoIP home phone VoIP services will default to High Bandwidth codecs like G.711u. This will not work over dial-up.
Standard Codecs that work over dial-up are G.729a, G.726, and GSM.
Skype uses a proprietary High Bandwidth codec and will Not work over dial-up. Just bear in mind that when using VoIP over dial-up, it will never be as good as over high-speed Internet. But, you can do it when there is no other option but dial-up (and I know many people these days are still stuck on dial-up Internet - for various reasons).
Here are some VoIP services that will work over Dial-up connections using your PC and a Softphone:
- CallCentric (with their free downloadable softphone) G.729a codec
- InPhonex (with their free downloadable softphone) G.729a codec
- Les.net (with a Softphone that supports G.729a or GSM)
- Voip.ms (with a Softphone that supports G.729a or GSM)
- Efonica (G.729a)
- PcCall (GSM ?)
- Google Talk (Jabber XMPP)
- Yahoo Messenger (not sure)