My father's computer recently just crashed and the files that he recovered from his laptop's hard disk are mostly corrupted. He's hoping to recover some files from his external hard disk, files that he has already deleted that is...

Do any one of you know of any reputable software for this task?

There are no sure-fire 100% success stories here, but I have had good luck with these:

Avira Unerase Personal – Official support discontinued, but still available from site
Recuva, from the makers of CCleaner.
Restoration

Hey Dig! Thanks for the links! I'll keep you guys posted on the status

Edit: Do you know if there are any way to fix corrupted files? Especially Microsoft Word documents.

It depends on how and how badly they are corrupted. You may be able to open with Notepad first, clear out any formatting then save as .txt file and try to pull it back into Word.

I found How can I recover a corrupt document or template - and why did it become corrupt? and Ms Word recovery for any corrupt Word document.

To repair your word files you need word repair software. The software I used last year to repair my corrupted word files was Stellar Phoenix Word Repair Software. It is very easy to use software. You can try this software to repair your corrupted files. What you need to do is just download the demo version first from here: Word repair software repairs, recovers corrupted or damaged Ms Word document / .doc files and scan your word documents. If you are able to view your files in preview mode then just opt for the full version and save your file.

Since almost 2 months has passed, I don't think it's a problem anymore.

But to be truthful, that Stellar Phoenix Word Recovery program gives me some concern. It's pretty expensive compared to competing products, but then if a lot of work went into the document, it may be worth it. I don't know. Certainly the data on my computer is worth much more than the computer. But I am a bit concerned with their marketing. While it is typical for free versions to offer limited recovery, Stellar is not clear on that. Here they say,

Please download a free version of the software to recovers your Word files with all its contents.

But here they say,

Saving the recovered files would require you to buy a full version of the software.

I just want companies to be upfront and honest with me. Clearly, you cannot "recover" these files with the free version. You can only view "recoverable" files. That may be enough, if you can retrieve the data you need. But to me, I don't want to view trashed files, I want to get them back - "recover" them so I can edit, print, copy, save or whatever.

MS Word Document Recovery Software and Undelete utility makes it clear what the free version will do, or not do for you.

I recommend anyone considering such programs use the free or trial versions first, and see with they find. Then, consider paying to fully recover.

Of course, a good backup routine can prevent a lot of headaches too.

Well, the files were never really properly recovered but my dad gave up. Slipped my mind to update this thread. Terribly sorry.

I've tried a few software that does exactly what you quoted. They show you what files they can recover, but won't let you do so unless you dish out the dough.

Slipped my mind to update this thread. Terribly sorry.

No problem.