The recommended way that you do this is to edit the page with FrontPage 2003 and delete the content.

Also,

You can delete the entire Quick Launch column using FrontPage 2003.

Or since each Quick Launch group is a separate linkbar so you can also just
remove individual groups.

You can even create your own Quick Launch groups. They won't be updated by
Windows SharePoint Services but they can be valuable. I often create a Sites
groups and add links to child sites. Or you could add a Miscellaneous group
with whatever links you'd like.

If you don't have (or want to use FP), another way is to update the style sheet. Just set (add) display: none on the navigation classes:

.ms-nav td, .ms-nav .ms-SPZoneLabel, .ms-input {
display: none;
font-family: Verdana, sans-serif;
font-size: 8pt;
}

This is how I was going to suggest doing it. The only thing is, this
will disable this for any site  or portal that uses this convention.
If you just want to do it on one page, the FP is the answer. If you
want it to go away everywhere, this style sheet rule is the way to do
it.

Another way is to copy this style out, then edit it and save it as
your own custom css file and then apply that style sheet to a site or
the portal. That way on any upgrades you are not editing MS files.
If you went this route, all you would need in the file is:

.ms-nav td, .ms-nav .ms-SPZoneLabel, .ms-input {
display: none;
}

Save that into a file and apply that to whatever.