BEST UPGRADE regardless of cost?

Changing my ARC VT100 MKIII for NAGRA VPA's. Like the difference between zipped and unzipped computer data.
This is a tuff question because the best updgrade is alwas the weekest link in the system. For some it is speakes for me it was my pre amp I went from a ARsp16 toa asteix clyspo. What a difference.
ARC LS-7 to Supratek Syrah

night & day.
In my personal audio history, the biggest improvement was when I replaced my Rectilinear III speakers with Thiel 3.6s. Of course, the improvement was expected. The biggest revelation to me was when I replaced my very cheap Monster Cable speaker wire with Audioquest Dragon silver. I had been skeptical that wire makes a difference, but this convinced me.
House with optimized listening room.
Cartrdigemans Isolator,
revelatory for $150 - wish I could afford one for all my tables
Getting rid of the nagging wife!
Well, with if I can answer this differently, if factoring in cost, the most effective upgrade was dedicated lines without a doubt. The cost? Only $400, but sonically worth thousands.
The Source. Always has been...always will be: the most down right major player in a system. Speakers a close second. With the advances in digital in the past few years, most new cd players today, can bring some added happiness to ones's tympanics...peace, warren
Perfecting the room acoustics. Made a bigger difference than any componant I ever bought or upgraded.
Re-thinking my answer, this time without regard to cost, I heartily agree with Warrenh. Other components have improved the sound of my system (some quite a bit), but nothing has increased the music I hear more than when I have upgraded my source.
For me the big one was the source, bringing my Linn Sondek Lp12 TT home back in 1983. It all gets back to, if you can't retrieve it in the first place, you'll never hear it with even the coolest speakers or amplifiers IMHO. Happy Listening!
Merlin VSM-MM speakers,best single purchase ever,in my system ....
Build a dedicated Audio room. You've never heard your system until you've done this. Get Rives Audio, Auralex, or ASC to help you and follow their recommendations. You won't believe the differnce.
Shakti-sonic hollgraph's- After 30 years as an enthusiast, these devices are the best upgrade I've ever made. Makes one realize just how critical the room acoustics are-and may stop one from the "endless" componment upgrade path. They are just staggering in their ability to create a lifelike stage in one's room. C
The room. Design and treatments from Rives Audio made a tremendous improvement.
Got to go with Sgr on this one. We are talking cost no object. Well that be some VERY serious $$.
I have to agree with the others concerning the source equiptment. Upgrading the turntable or even a CD player can work wonders. Of course all the equiptment must intergrate well with each other. If anyone wants to try a 'new' source component, may I suggest 4 track open reel factory pre-recorded tapes. This is real analog.
The best way to improve any electronic device is to improve the electrons upon which it feeds. Just as a Porsche 911 turbo will likely disappoint someone fueling it with kerosene, so most high end source components will disappoint anyone fueling them with the 120v hash they call power in North America. Put in a dedicated line for your system (20 amps minimum) before you give up on it. Now here's the "regardless of cost" upgrade. Buy the Burmester 948 power conditioner. It's the only one that truly improves the sound of equipment uniformly across the board. But it costs $6500. Every other "conditioner" is really a filter.
While room treatment is essential, if the singer is a dog, how better to hear her rabid salivations than the slap echo from your credit card?
The best upgrade is a balanced one, preferably the one that addresses the weakest links in your system. Short of that, it's like asking the question : Do you prefer to listen to a signal from a superb source that has been compromised by downstream components (including AC hash and room acoustics) or do you prefer to listen to the output of superb speakers that has been compromised by upstream components (and AC hash and room acoustics)? If the system is already fairly well balanced and you want to take it to the next level, I would agree with Warrenh: improve the source first. After that, it would depend on what the new and higher resolution uncovers. Experiment. If a weakest link is revealed, address it. If all the remaining elements are equally "weak" relative to the new source, upgrade the speakers next. There are no easy universal answers, unless you win the lottery...but then again...
A reel to reel tape player.

For myself there may be two I'd consider best. First being the acoustic treatment/taming the listening room and second a change of speaker cable.
This may be strange but I removed a Transparent Ultra from the system and replaced it with a vintage Tara labs and never looked back. Whoever bought the Ultra here on agon got it for pennies and I hope it works for them, it did nothing for me.
@khrys. I think your blanket statement on other AC power products is incorrect.   You might enjoy learning about balanced power from Equitech. Maybe :)
Spectral Pre and amp with MIT cabling. Spectacular improvement over the other “so called” top level equipment I had. I’m forever greatful to the well known,well respected Michael Percy (Audio) for his knowledgeable guidance. (PS for those unaware; both Spectral and MIT have extraordinary engineering talent whose expertise is respected by those in other fields :). 
I agree, treat your room!
The best upgrade I have done here.
Playing with speaker placement absolutely free, if you don't find improvement you can always replace to original location.
The speaker is the most inaccurate piece of gear in the system not to mention each one interacts with rooms differently 

the speaker is easily, hands down, the most variable product sound wise and thus has the most influence on how your overall system will sound. 

Fixing room acoustics is great, but a speaker that has muffled mids, or a recessed sound will always generally sound that way. 

It it makes me laugh when people say the front end is more important. It’s important no doubt, but unless your using the crappiest gear it’s not as important as the speakers.  This assumes there is no piece of gear in the system wildly out of synergy with the rest of the system. 

The the thing is I can put you in $100000 system with a $20000 amp $30000 set of speakers and change out the amp with a $1000 amp with the same power ratings, set it to the same dbl’s and you might notice some nuanced differences. But Change those speakers out to a different design type and there would be no doubt there are differences. 

The speakers make the biggest change in any given system assuming room acoustics are equal between systems.