My friend and I are traveling to Ireland in October. We are mostly staying along the coastlines, with the exception of a few destinations toward the middle of Ireland. Can we get around easily with buses, taxi's and trains relatively cheap? Thus the question, should we rent a car. We are staying in Ireland for 10 days. What do you think?
I have traveled around Ireland using only public transportation. But note that the Irish rail system is not very extensive, so most of the time you will need to use Bus Eireann to get to a lot of destinations. The bus network is very comprehensive and typically pretty reliable as far as getting you there on time. Of course, traveling by bus or train, you lose the flexibility to just stop and get out of a car if you see something interesting along the way.
You don't mention what your proposed itinerary is - where are you starting, what direction are you heading, do you need to get back to your start point to fly back home or did you fly open jaw? For a 10 day trip it might be best to try and keep your travel time down and base yourself out of just 2 or 3 cities or towns and take day trips (either via public transit, or there are plenty of day tour buses you can hop onto in the major cities like Galway or Dublin).
You also don't mention your age, which could be a factor in whether or not you would even be able to rent a car.