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
4 / 5
The Sons of HodirHated · 1,950 / 36,000
2 / 2
The SunreaversHonored · 9,862 / 12,000
1 / 2
The Wyrmrest AccordNeutral · 0 / 3,000
1 / 1
The Burning Crusade
16 / 16Complete
Cenarion ExpeditionNeutral · 2,015 / 3,000
1 / 1
NetherwingNo standing yet
6 / 6
Sha'tari SkyguardNo standing yet
5 / 5
The Mag'harNo standing yet
4 / 4
Horde
48 / 53
Bilgewater CartelFriendly · 348 / 6,000
1 / 1
Darkspear TrollsHonored · 2,194 / 12,000
7 / 8
OrgrimmarFriendly · 5,999 / 6,000
17 / 18
Silvermoon CityFriendly · 5,999 / 6,000
8 / 9
Thunder BluffFriendly · 3,448 / 6,000
7 / 8
UndercityFriendly · 5,698 / 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 3 hours ago. Some mounts may be missing or incorrect still. Please report any issues on the contact page.