Pandaren mounts are available on their corresponding race. Create a new character and you can get them without the standing.
Cataclysm
2 / 3
Hellscream's ReachNeutral · 750 / 3,000
0 / 1
RamkahenNeutral · 1,000 / 3,000
2 / 2
Wrath of the Lich King
0 / 5
The Sons of HodirHated · 1,300 / 36,000
0 / 2
The SunreaversFriendly · 2,829 / 6,000
0 / 2
The Wyrmrest AccordNeutral · 1,235 / 3,000
0 / 1
The Burning Crusade
7 / 16
Cenarion ExpeditionNeutral · 1,195 / 3,000
1 / 1
NetherwingNo standing yet
0 / 6
Sha'tari SkyguardFriendly · 3,630 / 6,000
2 / 5
The Mag'harNo standing yet
4 / 4
Horde
40 / 532 to get now
Bilgewater CartelFriendly · 5,999 / 6,000
0 / 1
Darkspear TrollsHonored · 3,692 / 12,000
6 / 8
OrgrimmarRevered · 2,792 / 21,000
14 / 18
Silvermoon CityFriendly · 3,795 / 6,000
7 / 9
Thunder BluffFriendly · 5,999 / 6,000
6 / 8
UndercityFriendly · 4,457 / 6,000
7 / 9
Darkspear Trolls and Orgrimmar and Silvermoon City and Thunder Bluff and Undercity mounts are available on their corresponding race. Create a new character and you can get them without the standing.
Standings come from the last update, about 9 hours ago. Some mounts may be missing or incorrect still. Please report any issues on the contact page.