Like RD said, you didn't have to be an
Elf to wear an Elven-ring.
Gandalf was a
Maia, a very powerful 'spirit', which took the form of an old man. Though he was not an Elf, and greater than an Elf,
the Ring was still advantageous for him.
The original bearer of the Ring, which is called
Narya, was
Cirdan. He gave it to Gandalf when he arrived at
Mithlond from
Valinor. This is what Cirdan said:
'Take this Ring, Master,' he said, 'for you labours will be heavy; but it will support you in the weariness that you have taken upon yourself. For this is
the Ring of Fire, and with it you may rekindle hearts in a world that grows chill. But as for me, my heart is with the Sea, and I will dwell by
the grey shores until the last ship sails. I will await you.'
---- Cirdan, LotR, The Appendices, Appendix B, "The Tale of Years, The Third Age"
So, basically, a lot of what helped Gandalf's tireless labours in his time in
Middle-earth, particularly during the
War of the Ring, was down to the Ring of Fire.
As it is the Ring of
Fire, there is much debate about whether this is what gave Gandalf his special ability with fire, such as on Caradhras and near the Gates of
Moria, where he lit up the
trees with fire from his staff. However, some people say that Ring was
only to "rekindle hearts", and real flames were not down to the Ring.
Elrond's ring,
Vilya, the mightiest of the Three, was originally
Gil-Galad's. But he also gave his to Elrond, so as you can see, giving up the Elven Rings to another was not uncommon.
Galadriel was the only one to keep her Ring for the whole time.