Excellent sounding LPs

Couldn’t say, but I don’t care about audiophile quality. I care about music. IOW, I don't play music to listen to my system. I play my system to listen to music.

FWIW: most of the upgrading I have done on my analog front end has been motivated by bringing out the best I can of all my old non-audiophile records, especially my classical collection. If all I cared about was fancy-pants boutique audiophile mastering/pressings I would have been done with upgrades a long time ago. The magic lies in the old run of the mill stuff; e.g. all my Philips classical records of the 70s. That stuff was really well recorded and sounds amazing with higher end gear.

It also pays to have an excellent record cleaning system.

Good question. I would say 98%+. And this has not always been true. My previous system which I used to refer to as my "Reference System", probably only 10 - 20 % sounded really good. I referred to it as my "Reference System" because it was so detailed and sensitive to the mastering and ambience of the recording. If anything was off I would hear it. Here is a vastly simplified version of one of the steps that took me from 10% to 98% sounding good. 

I upgraded my headphone system to a 300B high end headphone amp (Woo WA5). I was shocked at the power, warmth, and musicality of the sound. I remember listening to it the first time. Thinking... wow, that sounds great, I have to go listen to my main system to get the full impact and soundstage. I turned on my main system and it sounded terrible... flat, trebly... like missing the midrange... it was sterile and analytical. It was a $70K system that sounded like schiit in comparison to my headphone system. 

That was the end of my reference system. I immediately started building my next system with emphasis on sounding like "the real thing"... not hyper details and bass. I experienced a decade of season tickets to the symphony and lots of listening to individual unamplified instruments and small groups. What I built is incredibly compelling, musical and emotionally involving. Only albums that sound terrible will come across as such. All the details are there... they are just not highlighted and emphasized. The midrange is natural and fully bloomed. 

So, it is critical how you build your system as to the percent of recordings will sound good. 

True audiophile quality, not talking sounding good, 15%. When I had under 1k vinyl, purchased mainly in the late 60s and 70s, only 5% of those where of audiophile quality. Since then, I have now over 2k vinyl and 15% are of audiophile quality. That's because as my equipment got better, I got more conscious of looking for great music that was also specially well recorded. However done buying vinyl now. Lucky I started decades ago, prices have gone through the roof.

less than 10% for sure. I refuse to spend more than $20 for a record. My best ones never cost more than $15. But I only buy pressings from the last century.

+1, @ghdprentice 

The emphasis should always be on building a well-balanced system. That’s what truly allows you to get the most out of any playback format or component.