There is a short visit visa availiable to the following countries which is valid for two weeks. You will have to pay 20 Omani Rials (about US$50) at the airport.
Andorra, Argentina, Australia, Austria, Belgium, Bolivia, Brazil, Britain, Brunei, Bulgaria, Canada, Chile, Colombia, Croatia, Cyprus, Czech Rep., Denmark, Ecuador, Estonia, Finland, France, French Guiana, Germany, Greece, Hong Kong, Hungary, Iceland, Indonesia, Ireland, Italy, Japan, Latvia, Lebanon, Liechtenstein, Lithuania, Luxembourg, Macao, Macedonia, Malaysia, Malta, Moldova, Monaco, Netherlands, New Zealand, Norway, Paraguay, Peru, Poland, Portugal, Romania, San Marino, Seychelles, Singapore, Slovakia, Slovenia, South Africa, South Korea, Spain, Suriname, Sweden, Switzerland, Taiwan, Thailand, Tunis, Turkey, Vatican, United States, Uruguay and Venezuela.
Other nationalities will need to apply for a visa ahead of time at their nearest embassy or consulate.
Oman Visa information
Foreign embassies in Oman