Do I need to remove my wedding-band, which I wear every day, to wash for Hamotze or morning Negel vasser? What about other rings?
The Shulchan Aruch (OC 161:3) writes:
צריך להסיר הטבעת מעל ידו בשעת נט"י ( ואפילו הוא רפוי) (ב"י) ואפי' אינו מקפיד עליו בשעת נטילה, הואיל ומקפיד עליו בשעה שעושה מלאכה, שלא יטנפו (הרא"ש פ' תינוקת) (ונהגו קצת להקל אם הוא רפוי, אבל יש להחמיר, כי אין אנו בקיאים איזה מיקרי רפוי).
(My translation): You must remove your rings at the time of washing, even if you do not care to remove it while washing, since you care to remove it while working so it doesn't get dirty. Some are lenient because the ring is loose, but it is proper to be stringent because we cannot determine how loose is loose enough for the water to get through.
Summary: if you would take off your ring while working in dirt or something to keep it clean and safe, than you must remove it for washing. It is hard to determine how loose is loose enough to allow the water through. Therefor it is proper to always remove one's rings for washing.
I would clarify that last point by saying "Therefor it is proper to always remove one's rings for washing...if one is careful to remove it at other times as mentioned above." Even if most women are careful (and we would say batla daita), men might be less particular about removing bands.– YDKDec 30, 2011 at 16:17
I was taught that if you could not remove a ring then you do not need to do so. But if you can, you should. This applies to any rings that you're wearing.