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
RamkahenNeutral · 2,100 / 3,000
2 / 2
Wrath of the Lich King
2 / 5
The Sons of HodirHated · 1,430 / 36,000
1 / 2
The SunreaversFriendly · 726 / 6,000
0 / 2
The Wyrmrest AccordFriendly · 1,095 / 6,000
1 / 1
The Burning Crusade
0 / 16
Cenarion ExpeditionHonored · 5,921 / 12,000
0 / 1
NetherwingRevered · 7,237 / 21,000
0 / 6
Sha'tari SkyguardNo standing yet
0 / 5
The Mag'harNo standing yet
0 / 4
Horde
40 / 532 to get now
Bilgewater CartelFriendly · 5,046 / 6,000
0 / 1
Darkspear TrollsFriendly · 2,446 / 6,000
6 / 8
OrgrimmarFriendly · 2,641 / 6,000
14 / 18
Silvermoon CityFriendly · 5,046 / 6,000
7 / 9
Thunder BluffHonored · 24 / 12,000
6 / 8
UndercityFriendly · 5,955 / 6,000
7 / 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.