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
RamkahenNo standing yet
2 / 2
Wrath of the Lich King
5 / 5Complete
The Sons of HodirNo standing yet
2 / 2
The SunreaversNeutral · 650 / 3,000
2 / 2
The Wyrmrest AccordNeutral · 0 / 3,000
1 / 1
The Burning Crusade
16 / 16Complete
Cenarion ExpeditionFriendly · 3,089 / 6,000
1 / 1
NetherwingNo standing yet
6 / 6
Sha'tari SkyguardNo standing yet
5 / 5
The Mag'harNo standing yet
4 / 4
Horde
51 / 53
Bilgewater CartelFriendly · 5,999 / 6,000
1 / 1
Darkspear TrollsRevered · 17,083 / 21,000
8 / 8
OrgrimmarFriendly · 4,591 / 6,000
17 / 18
Silvermoon CityFriendly · 5,999 / 6,000
9 / 9
Thunder BluffFriendly · 4,216 / 6,000
8 / 8
UndercityFriendly · 5,999 / 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 5 hours ago. Some mounts may be missing or incorrect still. Please report any issues on the contact page.