If you don't use fiat, what are you exchanging? Bitcoins for...?
What? Are you serious?
For goods and services, and if you must have a physical store of wealth gold and silver.
Fiat is nothing more than modern day slavery. It is time for it to go the way of the dinosaur. They print it out of thin air with no finite level. With every dollar created $1.05 is owed to the banksters, thus ensuring debt slavery.
http://www.youtube.com/watch?v=lu_VqX6J93kI think there's some confusion over "exchange" here. Generally when people say "exchange" in relation to Bitcoin (or other commodities/financial instruments/currencies etc) they mean a service that allows parties to trade - e.g. an FX exchange allows parties to trade, say, GBP for USD, a commodities exchange allows JPY for gold, USD for oil, etc. The exchange acts as an intermediary between the two parties. MtGox, btc-e and BitStamp are all exhanges, LocalBitcoins is an "over-the-counter" (OTC) platform (no exchange, one party deals directly with the other party, with LocalBitcoins providing little more than an advertising-and-escrow service). (I'm wildly generalising here, but you should get the idea).
@CurbsideProphet - the above notwithstanding, alt coins!
Random comment: I've *never* bought BTC on an exchange. I've traded on exchanges before (I was really bad at it, as I was when I tried FX trading before BTC trading) but actual purchases of BTC have all been OTC - either through bitcointalk or LocalBitcoins. I'm not sure I'd change this, particularly after watching MtGox slow demise.