A Short Introduction to Prayer Beads
This introduction is going to be short and sweet. There is a lot to say and others have said it much better than I would. See, for example, Karen Deal Robinson's page in my resource links page. She's done a lot of work on this and presents it in a very informal and readable way. Or, the information at the Orthodox website that traces the invention of the prayer rope (arguably a precursor) back to St. Pachomius.
Prayer beads are found in many of the world's religious traditions. Their designs vary: some consist of repetitions of smaller groups of beads (e.g. the Catholic rosary and Baha'i prayer strands) while others have a representative number of beads (99 and 108 are common numbers).
Some of the numbers I've found:
The material sometimes matters. Some popular materials for prayer bead strings are Sandalwood and Rosewood, Tiger's Eye stones, glass, even bone. Some have meaning in certain traditions (for instance, in some Hindu practive, a rough bead is preferred over a smooth bead to represent the austere life one must follow), in others, the material is irrelevant (plastic rosaries for sale in gift shops). I haven't dug deeply into this question as I'm pretty sure that whatever symbolism it has will be lost on me.
Finally, there are different ways to use the beads. Most often they are used either as a way of keeping focused (as during walking meditations) or for repetition of prayers and mantras. Again, there is more information on this on the resource links page.