A person who normally requires eyeglasses for nearsightedness, farsightedness, or other visual disorders may wear eyeglasses on Shabbat in a public domain, even if there is no Erub. This applies even if the person can manage perfectly fine without the glasses. Since such a person wears eyeglasses "Derech Malbush," as a type of garment, he is not considered to be carrying them on Shabbat.
It should be noted that Rabbi Abraham Danzig of Vilna (1748-1820), in his work Hayeh Adam (56:63), forbade wearing eyeglasses in a public domain on Shabbat, out of the concern that they might fall off and one might then mistakenly pick them up, in violation of Shabbat. Clearly, however, he referred to a much different kind of eyeglasses than those which are normally worn today. Todays eyeglasses are held securely on the face around the ears, thus reducing the likelihood that they would fall. Therefore, one may wear eyeglasses in a public domain on Shabbat. This is indeed the ruling of Hacham Ovadia Yosef in his work Leviyat Hen (30).
This Halacha, however, does not apply to reading glasses. Since a person frequently removes his reading glasses and then places them back on his face, we must be concerned that one may remove the reading glasses in the public domain. It is therefore forbidden to wear reading glasses in the public domain on Shabbat.
The authorities debate the question of whether one may wear sunglasses in a public domain on Shabbat. Rabbi Moshe Halevi (Israel, 1961-2001), in his work Menuhat Ahaba (27:31), maintained that one may not wear sunglasses in a public domain on Shabbat, given the concern that he might remove them when he reaches a shady area. Hacham Ovadia Yosef, however, allows wearing sunglasses, provided, of course, that one ensures not to remove them in the public domain.
As far as contact lenses are concerned, Rabbi Moshe Halevi (listen to audio recording for precise citation) ruled that one may wear contact lenses in a public domain on Shabbat, so long as he has already grown accustomed to them. Before a person has grown accustomed to contact lenses, he often has to remove them to arrange them properly in the eye. Therefore, one should not wear contact lenses in a public domain on Shabbat until he has grown accustomed to them and wears them comfortably, such that there is no concern that he might remove them while in the public domain.
Summary: One may wear regular eyeglasses in a public domain on Shabbat, even without an Erub. This includes sunglasses, as well, but one must remember not to remove them when he reaches a shady area. Reading glasses may not be worn in a public domain on Shabbat. Contact lenses may be worn in a public domain on Shabbat only once the person has grown accustomed to them.
