I understand that some vestige of deleted files remains on one's hard drive. Can these (say sensitive banking details) be untraceably removed by simply filling the hard drive full with fresh (non-critical) files and then just deleting them to make space again?

Thanks.

No, you should use a 'shredder'. Cheap to buy or some vailable free online.

Naka.

Very clearly: NO!

Even if you use a program to override the whole HDD several times, let say 20x with 0 the data still traceable. Same is happens after formatting or partitioning! The real only way is to physicly damage the HDD! Like naka say: use a schredder but one which is schredding the HDD itself!!

You can use portable Eraser to do this.

Different erase schemes use a different number of passes and different write strategies. While recovery is "possible" by a forensic lab with some overwrite techniques, it's secure enough to safely get rid of the drive. With the most secure methods of overwrite, like the Gutman 35 pass strategy, recovery is essentially impossible. You certainly wouldn't need to worry about the local shop or a new owner getting the data back.

I would use this:

http://portableapps.com/apps/utilities/eraser_portable

More info about it here:

http://www.heidi.ie/eraser/