1. Please take a look at this Stack question. It points to a tutorial blog on how to do this.

In SPD open default.master, then add the script:

$(document).ready(function()
    {
    var form = $('form');
    if ( form.attr('action').indexOf('YOUR 36 character List ID - Without Braces') > -1 )
        {
        var checkbox = $('#ctl00_PlaceHolderMain_UploadDocumentSection_ctl03_OverwriteSingle');
        checkbox.removeAttr('checked');
        checkbox.parent().hide();
        var multiple = $('#ctl00_PlaceHolderMain_UploadDocumentSection_ctl03_UploadMultipleLink');
        multiple.hide();
        }
    }
);

2. There is another question on Stack here, where Falak Mahmood suggests that manually changing the Upload.aspx in 12/14 hive is not recommended. Instead, he suggests:

...to write a custom Feature which has AdditionalPageHead delegate control to un-check the "Overwrite existing file" (using jQuery) option while uploading the documents.

1. Please take a look at this Stack question. It points to a tutorial blog on how to do this.

In SPD open default.master, then add the script:

$(document).ready(function()
    {
    var form = $('form');
    if ( form.attr('action').indexOf('YOUR 36 character List ID - Without Braces') > -1 )
        {
        var checkbox = $('#ctl00_PlaceHolderMain_UploadDocumentSection_ctl03_OverwriteSingle');
        checkbox.removeAttr('checked');
        checkbox.parent().hide();
        var multiple = $('#ctl00_PlaceHolderMain_UploadDocumentSection_ctl03_UploadMultipleLink');
        multiple.hide();
        }
    }
);

2. There is another question on Stack here, where Falak Mahmood suggests that manually changing the Upload.aspx in 12/14 hive is not recommended. Instead, he suggests:

...to write a custom Feature which has AdditionalPageHead delegate control to un-check the "Overwrite existing file" (using jQuery) option while uploading the documents.