From the UK:

The main gateways are via St. Kitts, Antigua or St. Maarten. Excel fly from Gatwick direct to St. Kitts. There are various ways of making the short hop to Nevis either by ferry, water taxi or small aircraft. The Resort can arrange for the guest to be met at the St. Kitts airport and brought directly to the property by a combination of road and water taxis. British Airways (5 flights per week) and Virgin Atlantic have flights from London to Antigua, with connecting 25 minute flights to Nevis on WINAIR and LIAT (both scheduled services), or on Carib Aviation (charter service).

From Europe :

Air France has daily flights from Paris to St Maarten, with connecting scheduled flights on WINAIR to Nevis. Charters may also be arranged with Carib Aviation.

-NEW-
JETBLUE SERVICE

JetBlue Airways now offers direct daily non-stop service between Boston’s Logan International Airport and San Juan, effective December 13. This service will continue to operate through April 30, 2007.

From USA:

Many airlines including American, USAirways, TWA, Delta & Continental have direct flights from cities in the USA to San Juan, Puerto Rico. Passengers can connect there directly to Nevis on American Eagle or travel via St. Kitts on American Eagle or Caribbean Sun. During high season there are some direct charters to St. Kitts on TNT and GWV out of Boston and ATA Leisure out of Detroit. USAirways now have a weekly flight direct from Philadelphia to St. Kitts and have recently added Charlotte to St. Kitts on Saturdays.

From Canada:

Air Canada flies direct to Antigua. Guests may connect from there direct to Nevis on WINAIR, LIAT, or Carib Aviation . Signature Vacations have direct charters to St. Kitts in the Winter.