Do they really make a difference? Definitive answer is....

I have certain and unequivocal evidence that high quality cables and interconnects absolutely Do make a vast improvement... I heard it.  This is my second go around with set of nice cables - the first time I didn't realize how much of a difference the cables made because I bought all the equipment and the cables at one time.  this  go around im piecing things together as I go ...As soon as I put these cables on,   the transparency, imaging -things like the sound of the symbol being lightly struck by a drumstick (it's good to be king -Tom Petty) is round, full and has that distinct flavor..  quality cables are simply enriching to the system.   

thats how I feel
I've found some cables make a difference. I've rarely found cables worth their asking price.
Kudos on your discovery! You said it well, "quality cables are simply enriching to the system."

I suggest you look into aftermarket power cords, digital link i.e. USB, etc. for they, too, are as impressive in enriching the system as any others. If any of your equipment takes an outboard power supply such as wall wart, you will want to look into a dedicated, regulated power supply�. Yup, those also are enriching... and, of course, an aftermarket power cord on it as well.   :) 

What douglas_schroeder said, +1.       Although good hearing/listening abilities can cost one a bit more, with regards to their audio expenditures; the rewards are manifold.
Im glad to hear that (pun intended). I have a set Kenwood L-o7's im restoring/upgrading. I can't wait to hear the difference.  
Rodman- I studied with a trumpet professor down at Indiana university for several years. His primary philosophy was that hearing was a sensory development. In other words -the more you listen the more you hear. the rewards Ive gained from years and years of critical listening is something I can not put into words.

I have certain and unequivocal evidence that high quality cables and interconnects absolutely Do make a vast improvement

Fantastic.  We've been looking for good hard evidence for years!  All we've had are audiophile anecdotes saying "I heard a difference," the same "evidence" we get for green pens on CDs, mpingo discs, digital cables, and magic pebbles.

But you have unequivocal evidence!   What is it?

... I heard it.

Oh.  Yeah.  Thanks.  Glad that's settled. ;-)
"Oh. Yeah. Thanks. Glad that's settled. ;-)"

I know!  me too... and listen,  if anyone has any questions about anything else I know some little about,  Ill be glad to offer my empirical unequivocal universally sensory developed correct answer.  
(et lingua in maxillam)...I do love those cables though...
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For those that can hear the differences, no explanation is necessary.      For those that can’t, no explanation is possible.     NEVER stop listening and learning!
@sunnybaker -
An interesting anecdote re your Opera Consonance Joplin cable. This was the same brand that convinced me all wire does not sound the same.  Had previously been a skeptic..."Wire is wire, blah blah blah....".

Difinitive answer is ...NO 
If it's not or can't be scientifically substantiated with spreadsheets, shut the front door. Thankfully Quack marketing is not involved with the hospital industry, knee surgery might have you looking for a chair that works with knees bending backwards..Imagine that !
David Copperfield is a Magician..if you can fool the eyes why not the ears.