I have not heard good things about the
disneyland resort express. Apparently the drivers are rude, the shuttle is frequently late, and they only operate hourly, AND they could make several stops before they reach your hotel. They are not the cheapest either, as from lax, they cost 35$ per adult for roundtrip, and 20$ for one-way (kids 11 and under fly free). But I do know that some people have had good experiences with them.
There is also supershuttle. Basically, you can choose between a shared van and a private van. Shared vans pick you up at your terminal, then, if their 9 seats still are not filled, they circulate the airport several times before departing to Anaheim. Then they drop off the passengers wherever they neex to go. This option costs 17$ one-way. If you do not want to deal with the hastle of sharing vans and multiple stops, then you can reserve a private shuttle for 107 dollars one-way, flat fee. The vans will pick you up at the airport and simply take you to your destination without any stops.
Another option, not unlike private shuttles, are taxis. They cost about 90$ from lax to disneyland, but it could be more depending on traffic. Also, there are quite a few other privately owned shuttles that go the same route. Lots of people on the disboards seem to like zippy shuttle, which costs 80$ for 3 people, plus 5 $ for each extra person. The drivers are polite, they are quick and on-time, and really reliable. There are also Karmel and Lansky, as the PPs mentioned. For the private shuttles, you have to make a reservation, but for the public ones, you don't have to, but sometimes the driver of the public shuttle waits for you! Still, it might turn out to be a problem if your flight is delayed.
As for me, I prefer private shuttles, as getting to the resort as quick as possible-even if it means paying a bit more- is my top priority. But to save money, pick a public van!
Good luck deciding!