There are plenty of Reykjavik Airport Transfer options, including private taxi and regular bus.
Taxi in Reykjavík © Raf24~commonswiki / Creative Commons
A taxi from Reykjavik Airport to downtown Reykjavik is around 15000 Icelandic Kronas – that’s approximately $150 US Dollars for a 45 minute drive. You can book a Reykjavik Airport transfer online to be waiting for you on arrival, or you can simply join the taxi queue at the airport.
For a group of people, this can be reasonable, particularly or the convenience.
For single travellers or couples on a budget, the airport bus is a cheaper option. The bus takes longer than a taxi because it needs to wait for passengers to arrive at the airport and then drop off passengers at their respective hotels travelling on a circuit around Reykjavik.