Well, my best ever horse that I bred in GR2001 was named AA Nocturne, who I named after a real life black arabian stallion that I work with weekly. He was AMAZING. That's all I can say. Definitely the best thing I ever had in that game. However, his son, Vintage Legend, really wasn't much of a legend at all.

I never got GR 2003 because I couldn't find it at my local game store.

In GR2004, I have several who are to numerous to speak of separately, so I'll list them:
Silver Onyx
No Tomorrow
Cease Fire
Tempting Fate
Sweet Nothing
Easy Rhapsody
Easter Island
Absolut Logic
Skyy Bleu
Southern Comfort
Jack Daniels
Northern Dancer
Avatar
Black Gold(yes, the last three were named after real life racehorses)
Last Gemini
Loquacious Libra
Awful Aquarius
Arrogant Aries
Lawful Leo
Curious Cancer
Coy Capricorn
Tempting Taurus
Sinful Scorpio
Sly Sagittarius
Perfect Pisces
Vigilant Virgo

The last twelve were all from my mare Tempting fate, who managed to win a total of 10 titles, including king of kings. Also the only horse I may have a chance at winning the dream cup with(I've won the series, not the cup).

Namu