Most of the controls in sharepoint implement INamingContainer interface which essentially ensures the uniqueness of ID of the control no matter how it is used.  This is an Asp.Net concept and is not something that sharepoint is not a sharepoint only thing. Typically if your control needs to do something in script and is rendering the startup script or atleast rendering the call to that script the best way is to pass the ClientID in the call to that script. The value of ClientID can be obtained in the code behind and passed in when rendering the call to your script. The example below explains basically how to do it. The only gotcha is that the clientId value is only available after the control is added to the control collection.

For e.g
//Script
SomeSriptMethod(Id)
{
   var ctrl = document.getElementById(Id);
  //Do something with the control
}

//Html - Say this script is called by onClick handler on an "a" tag

<a onClick="javascript:SomeScriptMethod('ClientIdFromCodeBehind') href="">aaa</a>

Now the next thing is when your control is adding the hyperlink the code should kind of look like this

CreateChildControls(...)
{
    HyperLink link = new HyperLink();
    //Set  properties on the link as needed
   this.Controls.Add(link);
   //Note the clientId for link wont have the correct value till you add it to the control collection otherwise it will give you what you set in the Id for the link
   link.Attribute["onClick"] = "javascript:SomeScriptMethod(' + link.ClientID + "');" ;
   
}

Note: I am not doing any encoding but the control should do appropriate encoding of link.ClientID and this code wont compile and should be treated as pseudo code only.

Not sure I followed the 2nd post here, above.  How can you pass in and retrieve an ID using

var ctrl = document.getElementById(Id);

when you don't even know the ID in the first place because it's being made unique when rendered by SharePoint each time?  Wasn't that the whole point of this - to get an ID back for the control when you didn't know what the ID is, based on some other property the control has?

This would work if you use the "title" property on an input control, normally.....

function getTagFromTitle(tagName, title) {

// tagName = "input"
// title = the title given to the control

  var tags = document.getElementsByTagName(tagName);

  for (var i=1; i < tags.length; i++) {
    var tempString = tags[i].name;
    if (tags[i].title == title) {
      return tempString;
    }
  }
  return 'null';
}

The problem is that this kind of thing doesn't seem to work in SharePoint, at least for me, for bringing back anything.  I've tried

var tempString = tags[i].id;

and

var tempString = tags[i].name;

in that function above, so far, while passing in the title "Search Box" for the SearchCenter template to try and give me the ID or name for the search box, so I can get its .value and pass on the keywords.  Can't get anything out of it - searchTerm is null in the function below.  This script does work when used in VB 2005 against a regular, common, HTML input textbox control, however:

function getSearchTerm() {

var searchBoxElem = getTagFromTitle("input", "Search Box");
var searchTerm = document.myForm.elements[searchBoxElem].value;
alert(searchTerm);
}

When trying to use

document.getElementById('<%= ((TextBox)this.fvFormView.FindControl("Search Box")).ClientID %>')

I get the error:
 
An error occurred during the processing of /tsearch/default.aspx. Code blocks are not allowed in this file. 

Even commenting that code out didn't correct the error - had to delete that line altogether before I got my SearchCenter back up.

So what gives?  How are we supposed to get the values out of SharePoint controls?

Thanks code worked for me

function getMyElement(sName) {
try {
var aTagTypes = new Array("DIV", "INPUT");
sName = sName.toUpperCase();
for (var i = 0; i < aTagTypes.length; i++) {
var sTagType = aTagTypes[i].toString().toUpperCase();
var aEmts = document.getElementsByTagName(sTagType);
for (var ii = 0; ii < aEmts.length; ii++) {
var oOb = aEmts[ii];
var sID = oOb.getAttribute("id").toString().toUpperCase();
if (sID.indexOf(sName) > -1) {
return oOb;
}
}
}
} catch (e) {
alert("ERROR: " + e.Description);
}
return null;
}
 
function doThis() {
var s = getMyElement("Text1").value;
//alert("The value of this field is: " + s);
getMyElement("oDIV_02").innerHTML = s;
}

We want to add header breaks between editform input boxes based on strings in the column names. We are very close, but the insertbefore line does not execute.

The full post in under Technet Sharepoint - "Inserting a Table row with Javascript" user JCNET

<script type="text/javascript">
var theRows = document.getElementsByTagName("TR");
var r = 0;
var strTitle = "";
while (r < theRows.length)
{ try
{ strTitle = theRows[r].innerText || theRows[r].textContent;
strTitle = strTitle.replace(/\n|\r|\t|\^ /g,"");
var row = theRows[r],
cells = row.getElementsByTagName('td');
if (cells[0].className.indexOf('ms-formlabel') > -1) 
{
if (strTitle.indexOf("(HP)") == -1)
{
  theRows[r].style.display = "none";
}
 else
 {

 theRows[r].cells[0].innerHTML = theRows[r].cells[0].innerHTML.replace("(HP)","");
 
 if(/H\:/.test(strTitle))
      {
        var fheader = (strTitle.match(/\(H\:(.*?)\)/g));
        //var header = fheader.replace("(H:","").replace(")","");
        var header = fheader;
newrow=document.createElement('tr');
newcell=document.createElement('td');
newcell.appendChild(document.createTextNode(header));
newrow.appendChild(newcell);
        alert(header);
        r.parentNode.insertBefore(newrow,r);
        alert("Done");
}
 }
}

}catch(err){}r+=1;
}
</script>

or just explicitly set the id of the control in your code and the client-side code will work as expected:

txtTextBox1.ID = "txtTextBox1";

From then on:
document.getElementById('<%=txtTextBox1.ClientID%>');
should work properly in your client-side code