This is my first Yom Kippur as a married woman--I usually remove ALL of my jewelry, but I'm not sure about my wedding band (which conforms to halakha). Should I wear the wedding band but remove the ring my husband gave me as a gift, and which has stones in it? Or should I remove both?
In addition to the Mishna B'rura (cited in Sam's answer and based on the Matei Efrayim 610:9) that says "they should not adorn themselves with the jewelry that they wear on Shabbos and Yom Tov, due to the dread of the Day of Judgment," Rabbi Betzalel Stern (שו"ת בצל החכמה חלק ו סימן ג) explicitly says that a person may wear jewelry (such as a nice watch) on Yom Kippur if the person wears that jewelry throughout the week, as well.
As far as simple platinum rings, the metal usually does not contain any gold, so that should certainly not present the problem of wearing gold on Yom Kippur.
Again, please consult your local rabbi for a practical ruling, and/or ask other local women regarding the practice in your community.
The Mishna Brurah 610:16 writes women are noheg to also wear clean white clothes but not to wear jewelry that they wear for Shabbas and Yom tov for the greatness(fear) of the Yom hadin.
The Piskei Tshuvos brings Rabbi Akiva Eiger(hagoas) who writes that some places don't wear gold because of the egel ,but women did not participate in the egel.In Teivis Guma(Pri Megadim) since women receive support from their husbands we are noheg that no one wears gold.Also the Matteh Ephraim holds that the congregation is one as a whole.
However that was in reference to special type of clothing (white with gold around)but nowadays we don't have such clothing,jewelry would be ok as long as it is not worn specially for Shabbas and Yom Tov. See footnotes for many sources.
I'm not aware of a particular reason to avoid jewelry, so long as it's in good taste and not distracting (and if I'm not mistaken, there's a comment from Tosafot that at least in France 800 years ago, the women showed up on Yom Kippur with jewelry). I think I'd heard something as a little kid about gold being bad because of the Golden Calf, but that may have been a folk tale as I don't think I've seen it in any authoritative source. (Anyone else here want to help me with that?)
Have you looked around at what the other women in synagogue have done? If the other married women wear wedding bands and/or engagement rings, I can't think of why it would be a problem to do the same.