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
RamkahenNeutral · 0 / 3,000
2 / 2
Wrath of the Lich King
5 / 5Complete
The Sons of HodirNo standing yet
2 / 2
The SunreaversHonored · 6,354 / 12,000
2 / 2
The Wyrmrest AccordNeutral · 1,820 / 3,000
1 / 1
The Burning Crusade
16 / 16Complete
Cenarion ExpeditionFriendly · 817 / 6,000
1 / 1
NetherwingNo standing yet
6 / 6
Sha'tari SkyguardNeutral · 0 / 3,000
5 / 5
The Mag'harNo standing yet
4 / 4
Horde
48 / 53
Bilgewater CartelFriendly · 4,395 / 6,000
1 / 1
Darkspear TrollsFriendly · 5,395 / 6,000
7 / 8
OrgrimmarFriendly · 5,999 / 6,000
17 / 18
Silvermoon CityFriendly · 2,695 / 6,000
8 / 9
Thunder BluffFriendly · 5,395 / 6,000
7 / 8
UndercityFriendly · 2,795 / 6,000
8 / 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.