For loop error: Uncaught ReferenceError, variable is not defined. What's wrong?

Question 1

linkIdOn's scope is limited to cambioColorOnMouseover. But that is not your only problem. You need to move several things around.

My suggestion:

for(var linkId = 1; linkId < 5; linkId++) {
    document.getElementById('link'+linkId).onmouseover = function() {
        this.style.backgroundColor = "#eee";
        console.log(this.id);
    };
    document.getElementById('link'+linkId).onmouseout = function() {
        this.style.backgroundColor = "#ccc";
        console.log(this.id);
    };
}

For the benefit of others who don't know the CSS3 way to do this (which, though the OP wants to do this in JavaScript, is the preferred way):

#link1, #link2, #link3, #link4, #link5 {
    background-color: #ccc;
}

#link1:hover, #link2:hover, #link3:hover, #link4:hover, #link5:hover {
    background-color: #eee;
}

Though if you did the CSS, you would likely have a link class instead of using ids.

(I´ve changed two small typos that prevented the example to work (the system tells me that edits must be at least 6 characters) Thanks for your help! - Rosamunda)

Question 2

You probably want to do something like:

function linkOn() {
  this.style.backgroundColor = '#eee';
}

function linkOff() {
  this.style.backgroundColor = '#ccc';
}

window.onload = function() {
  var links = document.links;
  for (var i=0, iLen=links.length; i<iLen; i++) {
    links[i].onmouseover = linkOn;
    links[i].onmouseout = linkOff;
  }
}

though you are likely better off to add and remove a class so you can control the effect through CSS rather than script.