There's been some concern about Bitcoin transaction fees, lately, and the outlook appears grim. A new study by Dr. Kaskaloglu claims that our low fees are unsustainable, and Gavin Andreson's proposed new system could raise them drastically. While changes will need to be made, eventually, most of this F.U.D. is unnecessary, and contrary to the ideals of Bitcoin.
What's true is that Bitcoin miners are subsidized by the reward for producing a block, and that the supply of new bitcoins decreases every 4 years. This will make miners increasingly reliant on transaction fees. A century and a half from now, transaction fees will be their only income, so how do we insure that people will continue to be willing to mine for coins? The extra work required to process another transaction is actually quite negligible--the reason a miner might choose not to include yours in his or her block is that they can only fit so many. Unless your transaction is marked "high priority" (for which designated space is reserved in each block) by the network, it will not be included if enough other transactions offer a higher transaction fee. This leads to a free-market competition in which impatient Bitcoin users compete for who is willing to pay the most, as Satoshi intended.
The problem here is that Bitcoin's appeal is partially the facilitation of microtransactions: people rely on low transaction fees in developing countries and when tipping other users. Even if they're willing to wait for more confirmations, transaction fees must be competitive with state-backed solutions, and 0.002 BTC (the upper extreme suggested by Gavin) doesn't cut it. Somehow, miners need to make more money from transaction fees, or not enough people will mine for the network to be secure. Raising fees, however, is no the only way to do that.
What's important to remember is how far away this is from happening. Despite the doom and gloom, those with expertise or investments in Bitcoin mining seem relatively unconcerned. "It's an issue that will have to be dealt with after a few more block reward halvings," said Bryan Hellard of Newnote Miners. "We have at least 10 years."Cryptocurrency is reaching the cusp of adoption right now, and if Bitcoin's exponential price trend continues, the price of a Bitcoin should be orders of magnitude higher by then. The most likely reason otherwise would be that another cryptocurrency has been stealing the spotlight, which it would be unlikely to do without offering negligible fees. It's worth pointing out that cryptocurrency itself is prone to free competition, and the possibility of losing premier status will motivate the Bitcoin development team to update Bitcoin with a solution.
If an altcoin does manage to solve the problem with some radical new protocol, then we've really not much to worry about. Otherwise, it will be decades before block rewards are too little to incentivize mining. Serious issues like quantum computing will have arisen by then, and the physical Internet network will be far more advanced.
Bandwidth will likely increase to the point that relaying more transactions per block isn't very expensive--I'd argue that it's inevitable, as the percentage of people using bitcoins increases. The system will otherwise grind to a halt. Since the bulk of processing work done is not in processing the transactions themselves, this will mean that miners make more money from transactions by increasing transaction volume. A successful and growing Bitcoin necessarily implies that more transactions are being made, as Bitcoin increasingly becomes the method of choice for online and offline payment. The development team will have no choice but to increase the data size limit for blocks to be accepted, allowing more commerce to be done--and taxed by the miners.
Rejecting transactions means rejecting income, and it's futile if other miners--which they will--are willing to accept it. Some might stop mining in response, but that leaves more money for the rest, and there will always be enough miners to keep the network secure. If that ceases to be the case due to some intrinsic deficiency with the Bitcoin protocol, it will adapt or die. That's what Satoshi would want.