Pandaren mounts are available on their corresponding race. Create a new character and you can get them without the standing.
Cataclysm
1 / 32 to get now
Hellscream's ReachHonored · 850 / 12,000
1 / 1
RamkahenNo standing yet
0 / 2
Wrath of the Lich King
3 / 5
The Sons of HodirRevered · 2,422 / 21,000
1 / 2
The SunreaversNeutral · 612 / 3,000
1 / 2
The Wyrmrest AccordNo standing yet
1 / 1
The Burning Crusade
16 / 16Complete
Cenarion ExpeditionNo standing yet
1 / 1
NetherwingHonored · 1,475 / 12,000
6 / 6
Sha'tari SkyguardHonored · 8,100 / 12,000
5 / 5
The Mag'harNo standing yet
4 / 4
Horde
49 / 533 to get now
Bilgewater CartelRevered · 7,266 / 21,000
0 / 1
Darkspear TrollsNo standing yet
8 / 8
OrgrimmarNo standing yet
17 / 18
Silvermoon CityNo standing yet
8 / 9
Thunder BluffNo standing yet
7 / 8
UndercityNo standing yet
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, 2 days ago. Some mounts may be missing or incorrect still. Please report any issues on the contact page.