Taxing aircraft fuel (kerosene) or introducing some equivalent charge is necessary both to reduce greenhouse gas emissions from aircraft and to level the playing field for other forms of transport. Such charges can be "fiscally nuetral", i.e. if you gather more money from fuel taxes you can reduce other taxes such as those on income.
If you have already clicked on the world map to indicate your proposed journey, you can see here how much tax you would pay if aircraft fuel were taxed at the same rate as petrol in the UK. Yet this level of tax is still far too low to have a significant effect on greenhouse gas emissions.
Imposing a kerosene tax is difficult because if one country introduced such a tax unilaterally, planes would just fill up in the neighbouring country where fuel was cheaper. Moreover, the rules of the International Civil Aviation Organisation (ICAO, a UN body whose purpose is to promote the growth of air transport) forbid any country from imposing a kerosene tax.
However there are ways around this obstacle. For example, the European Union has drawn up proposals for an EU-wide landing charge which would not be a flat rate, but instead be carefully calculated to reflect the greenhouse gas emissions and other pollution impacts from each particular flight (for flights beyond the EU, this would be doubled to take the return journey into account). Implementation of these proposals has been delayed due to the recent sacking of european commissioners.
Another approach is to bring greenhouse gas emissions from aircraft into the national quotas for greenhouse gas emissions agreed under the Kyoto protocol of the UN Climate Convention. The problem is that policymakers cannot agree which country is responsible for the emissions from international flights -the country of departure, of arrival,or the one that sold the fuel. Therefore emissions from international air and sea transport (known as "bunker fuels") are completely exempt from the emissions limitations agreed in the Kyoto protocol (this loophole creates some strange anomalies -for example internal flights in the USA are included in the USA budget, wheras transatlantic flights and those between European countries are not).
One way around this problem is, instead of allocating the emissions to any one country, to require airlines to purchase emissions quotas from any government, since these quotas will be tradable. This option is discussed further in the "Proposals for a principled protocol" written by the Global Commons Institute (GCI).
An advantage of tradable quotas, is that the total emissions are constrained in advance, and the market price will adjust itself accordingly, whereas when setting taxes we can only guess in advance what level will achieve the desired outcome. Moreover quotas are garuenteed to be fiscally nuetral, whereas international taxes require a global government to decide how to spend the money. However the acceptability of tradable quotas depends entirely on whether the initial distribution of quotas is recognised as equitable. This issue is discussed further in GCI's web site
Taxation options are discussed in more detail in the web page of "The Right Price for Air Travel", a campaign run by Friends of the Earth (Netherlands), which also has news of campaigns on this issue from all around the world.