You'll remember Domenici, of course, as the senator (along with NM Rep. Heather Wilson) who was haranguing US Attorney David Iglesias to bring phony "voter fraud" indictments in the state via several inappropriate phone calls prior to the 2006 election. Iglesias was later fired for not having done so.
Like most Repubs, when called out, he'd rather run (or not run, as the case may be) than fight.
Though Cillizza speculates that NM Gov. Bill Richardson would be the "dream candidate" to run for the seat, it seems he's currently too busy for the moment running for vice president. We'd be delighted to see him change his mind and do something actually useful for the country in 2008.
UPDATE: AP confirms, and notes that "Domenici would be the fifth Republican senator to decline to seek a new term." They've also got more details on the "health issues" that Domenici, who had previously planned on running again, will use as his excuse. We guess "need to spend more time with the family" is getting a bit worn out by now.