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 ReachFriendly · 4,491 / 6,000
0 / 1
RamkahenNo standing yet
2 / 2
Wrath of the Lich King
1 / 5
The Sons of HodirNo standing yet
0 / 2
The SunreaversRevered · 6,484 / 21,000
0 / 2
The Wyrmrest AccordFriendly · 55 / 6,000
1 / 1
The Burning Crusade
0 / 16
Cenarion ExpeditionHonored · 4,289 / 12,000
0 / 1
NetherwingNo standing yet
0 / 6
Sha'tari SkyguardNo standing yet
0 / 5
The Mag'harFriendly · 1,594 / 6,000
0 / 4
Horde
42 / 53
Bilgewater CartelFriendly · 5,999 / 6,000
0 / 1
Darkspear TrollsFriendly · 5,999 / 6,000
6 / 8
OrgrimmarHonored · 4,593 / 12,000
16 / 18
Silvermoon CityHonored · 5,369 / 12,000
7 / 9
Thunder BluffFriendly · 5,149 / 6,000
6 / 8
UndercityFriendly · 5,999 / 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 15 hours ago. Some mounts may be missing or incorrect still. Please report any issues on the contact page.