Maybe the most widely used word is "Блядь" (whore, slut, bitch). In whole it means a woman of sexual work, but Russian people often use that word without any context, just to express any dissatisfaction, indignation, or fright, even pain. As euphemism you can use "Бляха-муха" (wodr-for-word, Plate-Fly)

It seemed that people here mostly don't understand what does euphemism mean)) Guys,euphemism is neutral word used instead of rude! I suppose that this link will answer on your question in details. http://ru.m.wikipedia.org/wiki/%D0%AD%D0%B2%D1%84%D0%B5%D0%BC%D0%B8%D0%B7%D0%BC

Блин instead of блядь, пиздец. Фигня, хрень = хуйня.

Вместо "х.й" (dick) - хрен, хер (уже само стало ругательным). ёперный театр, еще)

Here're some phrases instead of the well-known "блядь": ёкарный бабай, ёж твою медь, ядрёна вошь, писец, пипец, ёшкин кот. If not to say about curse words only, then it's more polite to say пожилой, зрелый instead of старый; нетрезвый instead of пьяный; нуждающийся instead of побирушка or бедный; одно место instead of уборная; etc.