[TolkienGurl]

They are
"slaves of the Nine Rings"
"ensnared by their lust for power"
"totally subservient to their Master"

They "individually accepted from him Rings of Power, made, so Sauron said, to give them power over all other Men and and to give long life; and by this means he trapped them, for the Nine Rings of Power were also designed to enslave their wearers."

The Rings lengthened their days. Death was denied, and life became unbelieveably wearisome. The only power they gained was that of terror "...for unable to relinquish their Rings, the Nine Lords became in the end wraiths..."

Basically all the Rings except the Three and the chief of the Seven were suseptible to the One, for Sauron had a hand in their making. He corrupted and distorted them to a great extent, giving the Rings many powers of mind and hand.

Note: for some odd reason, the Dwarves were insuseptible to the power of the One. Their days were not lengthened, as were the Nine.

"The nature of the Ruling Ring was such that by its power Sauron was able to dominate and enslave the Nine."

Exerpts from The Tolkien Companion.