Would this work... or it already exist

So i wa wondering since u can call someone using internet (with skype or something similar) would this work if one made a kind of gadget with basic functions like a cellphone but worked over the internet connection. Since wifi will be more and more available, if you install on that device a software like skype or voip stunt then people would be abble to call each other without having to pay any $ and more they could go on the internet and all for free (all they would have to do is just to buy the device). I was thinking hwo i could achieve a similar device but my knowledge in electronics isn’t enough advanced. Also, i was still thinking about how a person would recognize the other number since there would be no official communication provider ( u know like those big company like bell or verizon, att etc). I first though about using the same way like msn but that will mean that whenever you have to call, then you have to be sure that the personn is connected…and also i’m thinking about security issues…