I'm glad you included an image of the operation in progress, because it makes it easier to clear up some confusion and answer your question. I think previous respondents missed the fact that you're actually working in SharePoint Designer 2007 -- not Central Administration or the command line.
First, let me clear up some confusion: the operation you're carrying out through SharePoint Designer 2007 (SPD) is not actually a backup. Even though the menu item lists the operation as "Backup Web Site," what you're actually doing is creating an export - not a backup. This is important for a couple of reasons:
Export operations from within SharePoint leverage the Content Deployment API (aka the "PRIME API") and are not full-fidelity. Things like workflow state, alerts, and some other items will not be captured by an export.
When it comes to getting data out of SharePoint for protection, export operations are among the slowest mechanisms available compared to the standard backup operations.
Should it take 16 hours or more to export your data? Believe it or not, it certainly can. In tests that my team ran for export speeds with SharePoint 2007 (we work on a commercial backup product), it wasn't uncommon to see 10+ hours for a 100GB site collection. The actual amount of time it takes is dependent upon the nature of the data being backed-up, the amount you have, your hardware capabilities, etc., but 16 hours isn't unheard of.
If I had to guess, your export is probably stalled-out. While SharePoint is generating the export package (one or more .cmp files), they are temporarily being written to the site collection you are "backing up" unless you specified an alternate location using the "Advanced ..." button prior to the start of the operation. If your administrator has any sort of reasonable quota in-place, all those temporary files probably ran the site collection up to the max and caused the operation to seize.
So, now that you know what's actually happening in your case, here's what I suggest: if you need to back up or get data out of SharePoint 2007, your options (from fastest to slowest) are:
catastrophic backup > site collection backup > export
Each of these operations can be performed from the command line through STSADM. If you want to perform a backup (rather than an export) using a UI, only the catastrophic backup (farm backup) option will be available to you through Central Administration. Note: if you were using SharePoint 2010, you'd have PowerShell and some other Central Admin options available to you.
Some tips on each:
Catastrophic (full farm) backup:
If all you need is a site collection, you'll still have to grab the entire database containing the site collection. The backup/restore API doesn't get any more granular than the database level. Still, your backup will be faster than either a site collection backup or an export, and it can be restored to your current farm (if there's loss) or ported to another farm without issue.
STSADM.exe -o backup -directory <UNC path> -backupmethod <full | differential> -item <ID of the target database>
Site collection backup:
This method has been pointed out by a couple of respondents, and it will generate a single .bak file that is a backup of your site collection only. This backup method actually punches down to unmanaged code to operate, and it is still significantly faster than performing an export. Worth mentioning is that Microsoft does not recommend this option for site collections that are larger than 15GB in size, though you can make it go significantly farther than recommended.
STSADM.exe -o backup -url <site collection URL> -filename <name of backup file to create>
You've already seen this first-hand. It's great for granular (item-level) data, but pretty poor and slow for capturing entire site collections. You can do this through SPD (as you were doing) or with STSADM.
STSADM.exe -o export -url <site collection/site/list to export> -filename <export file name>
If you aren't a farm and server administrator, I'll tell you straight away: you're going to be out of luck with regard to the methods I mentioned (Central Administration and command line options). You'll need to enlist the help of your (hopefully) friendly SharePoint administrator to carry things out on your behalf.
I hope that helps!