You can catch an old style Routemaster on the number 15 Heritage Route and you can catch the new style Routemaster buses on the following routes:

The number 3 - Crystal Palace to Conduit Street
The number 8 - Oxford Circus to Bow Church
The number 9 - Hammersmith to Aldwych
The number 10 - Hammersmith bus station to King's Cross St. Pancras
The number 11 - Liverpool Street station to Fulham Broadway
The number 12 - Dulwich to Oxford Circus
The number 15 - Trafalgar Square to Blackwall DLR
The number 16 - Victoria station to Longley Way
The number 24 - Hampstead Heath to Pimlico
The number 38 - Victoria to Hackney
The number 55 - Oxford Circus to Leyton
The number 59 - Telford Avenue to King's Cross station
The number 68 - West Norwood station to Euston bus station
The number 73 - Victoria to Stoke Newington
The number 88 - Camden to Clapham
The number 137 - Oxford Circus to Streatham Hill
The number 148 - Camberwell Green to White City bus station
The number 149 - Edmonton Green bus station to London Bridge station
The number 159 - Streatham station to Marble Arch
The number 168 - Royal Free Hospital to New Cross/Peckham
The number 390 - Notting Hill Gate to Archway
The number 453 - Marylebone station to Deptford Bridge

You are able to use the Oyster card on both the London Underground and the new style Routemaster buses.