It is possible to get a 15 day, 30 day and 90 day visa at all points of entry into Nepal including land borders as well as airports. The price changes rapidly and it is cheaper to get a longer visa rather than renew the visa in Kathmandu. The procedure is normally simple and quick.
Flying out of Nepal.
Airlines can’t issue you a ticket at all unless you have the visa for the country you are flying to, or the country has a visa on arrival scheme.
Many airlines cannot issue you a one way ticket unless you have onward visas.
Embassies in Nepal for Onward Travel:
In 2009 it doesn’t look like even these are possible because of the unrest and government clampdown in Tibet.
Group visas mean that everyone on the group visa must cross every checkpoint together. If you’re not all there you have to go back.
Every group must have a Chinese/Tibetan guide with them who they must stay with at all times. We were quoted $3500 dollars per person to get to Ali in Western Tibet.
If you enter Nepal with a valid Chinese visa you can’t use it to enter China from Nepal!!
India also has an embassy and it is possible to get 3 or 6 month visas although the procedure is complicated and takes time.
See the individual country pages for requirements.