Is There An Initiative To Sequence The Genomes Of Critically Endangered Species?
The seedbank terdon mentions is the Norwegian Svalbard Global Seed Vault located at Spitsbergen island:

http://en.wikipedia.org/wiki/Svalbard_Global_Seed_Vault

However, the closest thing to a concerted initiative for sequencing animals I know of is the Genome 10K project:

http://genome10k.soe.ucsc.edu/

Their list of first 101 vertebrata proposed for sequencing contains 29 species with status RED from the red list. Most of them are only proposed, but the sequencing of the following are already in progress:


crested ibis (Nipponia nippon)
Amur tiger (Panthera tigris altaica)
cheetah (Acynonyx jubatus)
lion (Panthera leo)
domestic yak (Bos grunniens)
bactrian camel (Camelus bactrianus)


and that of the Chinese softshell turtle (Trionyx sinensis) has funding secured. Already complete are the giant panda, the chiru, and the polar bear.

And some surprising fact: where the funding is secured it is/was funded by the Beijing Genome Institute. A shame if this would remain the only one.