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 ReachNo standing yet
0 / 1
RamkahenFriendly · 4,977 / 6,000
2 / 2
Wrath of the Lich King
3 / 5
The Sons of HodirHated · 1,430 / 36,000
0 / 2
The SunreaversHonored · 4,429 / 12,000
2 / 2
The Wyrmrest AccordNeutral · 1,215 / 3,000
1 / 1
The Burning Crusade
0 / 16
Cenarion ExpeditionHonored · 6,040 / 12,000
0 / 1
NetherwingNo standing yet
0 / 6
Sha'tari SkyguardNo standing yet
0 / 5
The Mag'harNeutral · 2,536 / 3,000
0 / 4
Horde
40 / 538 to get now
Bilgewater CartelFriendly · 5,999 / 6,000
0 / 1
Darkspear TrollsHonored · 299 / 12,000
7 / 8
OrgrimmarNo standing yet
17 / 18
Silvermoon CityHonored · 274 / 12,000
4 / 9
Thunder BluffFriendly · 5,999 / 6,000
4 / 8
UndercityHonored · 2,287 / 12,000
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 9 hours ago. Some mounts may be missing or incorrect still. Please report any issues on the contact page.