The Seven and the Nine

The Seven and Nine Rings were originally made by the Elves and not evil until Sauron forged the One and later took these rings by war. Their initial purpose was to slow the passage of time and preserve beauty, but since Sauron had a part in their making they became accursed and had evil powers. He gave the rings to different races of Middle-earth to enslave and so control them.

Sauron gave the Seven to the Dwarves, who proved harder to enslave:

"They ill endure the domination of others, and the thoughts of their hearts are hard to fathom, nor can they be turned to shadows. They used their rings only for the getting of wealth; but wrath and an over mastering greed of gold were kindled in their hearts..." [The Silmarillion]

This implies their rings had other powers but were not used probably because this would draw attention to the user and all that he did.

Sauron gave the Nine to Mortal Men who proved easiest to ensnare. It was said that:

"Those who used the Nine Rings became mighty in their day, kings, sorcerers, and warriors of old. They obtained glory and great wealth... They had, as it seemed, unending life, yet life became unendurable to them. They could walk, if they would, unseen by all eyes in this world beneath the sun, and they could see things in worlds invisible to mortal men..." [The Silmarillion]

According to The Letters of J.R.R. Tolkien #131, the Seven and Nine conferred invisibility to the user as well as unending life. However, eventually the user would fade and become a wraith under the control of Sauron, the Dark Lord. However, the Three Elven Rings did not confer invisibility.