Let me show you my opinion on some software useful for photography. And I like it to have yours.

The main program I use is Photoshop, but I also use other small ones for specific tasks.

1.- What's the software you prefer to compare and find duplicate pictures?
I have tested many and I've picked this:

Double Pics 2.3 (slow but with many options)
Dup Detector
Pixels 1.5.1
Visual Similarity Duplicate Image Finder
Image Dupeless

I've also tried
Alike 2.2 (It doesn't detect all images)
Duplicate Image finder (It doesn't detect all images)
Dup Detector (lacks of automatic selection)
many other are too slow or simply don't work.

2.- What's the best one to improve the picture quality or remove noise?
DCE autoenhance
Neat Image
Noise ninja
They are not really automatic, don't offer really good results and sometimes
are difficult to use..

3.- ... to remove red eyes?
Anti red eye
Fred Miranda Red Eye Removal v1.1 Action for Ps
Red Eye Remover v1.4 (and other brands)
Photoshop filter - red eye pro1.1
Cutting & pasting other eyes.
Do you prefer Photoshop plugins or standalone programs?

4.- What about intelligent picture compression?