Pandaren mounts are available on their corresponding race. Create a new character and you can get them without the standing.
Cataclysm
3 / 3Complete
Hellscream's ReachNo standing yet
1 / 1
RamkahenFriendly · 4,127 / 6,000
2 / 2
Wrath of the Lich King
5 / 5Complete
The Sons of HodirNo standing yet
2 / 2
The SunreaversHonored · 1,808 / 12,000
2 / 2
The Wyrmrest AccordNeutral · 2,184 / 3,000
1 / 1
The Burning Crusade
16 / 16Complete
Cenarion ExpeditionFriendly · 2,960 / 6,000
1 / 1
NetherwingNo standing yet
6 / 6
Sha'tari SkyguardNo standing yet
5 / 5
The Mag'harNeutral · 2,938 / 3,000
4 / 4
Horde
53 / 53Complete
Bilgewater CartelHonored · 3,414 / 12,000
1 / 1
Darkspear TrollsHonored · 1,099 / 12,000
8 / 8
OrgrimmarHonored · 9,529 / 12,000
18 / 18
Silvermoon CityFriendly · 5,752 / 6,000
9 / 9
Thunder BluffHonored · 5,828 / 12,000
8 / 8
UndercityFriendly · 5,999 / 6,000
9 / 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 4 hours ago. Some mounts may be missing or incorrect still. Please report any issues on the contact page.