I've never used the Disneyland Resort Express service. This motorcoach service connects Orange County's John Wayne Airport (SNA) with the Anaheim Resort. For information, see http://airport.anaheimsightseeing.com/ (Disneyland Resort Express also connects LAX to the Anaheim Resort.)
For other options, see the John Wayne Airport website at http://www.ocair.com/ and click on Ground Transport.
In the past I've taken Super Shuttle. Its very big in California. Its safe and fast. It is a fleet of vans that hold about 10 people each. You can make reservations online. Search for super shuttle
We used the Disneyland Express bus in November and were happy with the service. Sure you do have to spend some time waiting for the bus to come, but we didn't mind the inconvenience.
The couple of times we have flown into John Wayne airport, we have taken a taxi. It cost about $35-$40 one way...but was very convenient. As soon as you get your bags, you go outside and there are usually a line of them waiting.
How long are you staying? My DSis and her husband fly into John Wayne from SFO, and the car rental runs them less than $20 a day for an economy car. Makes it less expensive than any other option for a weekender.