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
RamkahenFriendly · 2,394 / 6,000
2 / 2
Wrath of the Lich King
5 / 5Complete
The Sons of HodirFriendly · 2,225 / 6,000
2 / 2
The SunreaversRevered · 3,009 / 21,000
2 / 2
The Wyrmrest AccordNeutral · 1,850 / 3,000
1 / 1
The Burning Crusade
16 / 16Complete
Cenarion ExpeditionHonored · 11,199 / 12,000
1 / 1
NetherwingNo standing yet
6 / 6
Sha'tari SkyguardNeutral · 2,085 / 3,000
5 / 5
The Mag'harHonored · 390 / 12,000
4 / 4
Horde
52 / 53
Bilgewater CartelFriendly · 4,812 / 6,000
0 / 1
Darkspear TrollsRevered · 1,217 / 21,000
8 / 8
OrgrimmarNo standing yet
18 / 18
Silvermoon CityRevered · 1,291 / 21,000
9 / 9
Thunder BluffNo standing yet
8 / 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.