What is the  best mare or filly of all time?

Ruffian - hands down.  She and Secretariat were the 2 greatest race horses.

Zenyatta. She won 19 out of 20 consecutive races. She came in second for the first time ever on her final race at the Breeders Cup Classic, then retired. (I watched the race, and couldn't believe it, it was like she had this champion over-confidence problem, as although she would always take her time during the race and win in the final stretch, this time, she waited too long to kick it into high gear, and ultimately she only lost by inches). She was a mare. Never raced as a filly, I believe, as she was born in 2004, and didn't start her racing career until the very end of 2007, so was already past the age of 3 by the time of her first race. She's still alive and making baby future race horses. She's given birth to at least 6 foals since her retirement in 2010 and currently has another on the way.

Best for what?  Horse racing?   Endurance riding?  Dressage?  Roping?   Barrel racing?   Not enough information to answer your question.  

This depends on which country you live in, as well as which sport you're talking about. In the US, in Thoroughbred racing, I would say it was Zenyatta, with a few other exceptional mares close behind. If you're talking about other horse sports, such as eventing, for example, then I would say Bally Cor, and in the case of show jumping, Touch of Class and Miss Budweiser.

In Australia, it would be Black Caviar and the great mare Winx.

I think the Race Horse Red Rum, won the grand national in England 2 times and the Scottish national

and the Welsh national too was a mare and when it died it was buried at the winning post at Aintree racecourse.  

i hate nightmares some days.

Winks ( an australian mare who won 25 races straight and is now out to stud till she can't have anymore foals.