Right now, we still get a pretty quick response even if we don't pay transaction fees. But if the network ever started getting clogged, you could pay a small transaction fee to be given higher priority. In the future, it is possible that transactions without fees take days, while transactions with fees go much quicker.
As the volume of transactions gets higher and the incentive for finding blocks gets lower (bitcoins per block get divided by 2 every 4 years, and difficulty is rising quickly), isn't there a risk that in the future, fees become the main incentive, increase dramatically in price (and also become unavoidable)? Then doing a bitcoin transaction would be for rich people only. We certainly don't want Bitcoin to become a rich people tool those who can afford the high taxes.
Yes, that is a possibility. But since the network is open, you can always assume that someone will be mining and taking free transaction, for the good of the network. It might take a while to get confirmed, but it'll go through sooner or later. And if transaction fees were really getting high, that is just incentive for more miners to get involved. If people are leaving the bitcoin network because of high fees, then miners have a reason to try accepting more low fees, to keep the network alive. It should all work itself out. The future structure of fees isn't yet completely clear, and everything is still tweak-able.