Depends on the number of people you are talking about. I usually fly into Orange County (John Wayne) and just take a cab. From LAX, I know the Disneyland Resort Express is a popular choice, but I don't know the pros and cons of it. You should probably ask this on the Disneyland Resort board - the folks there know DLR in and out.
I've used super shuttle a couple of times. I believe the price was $17.00 plus tip for Shared Ride Van Service (from LAX to the Grand Californian).
I didn't have a reservation from the airport (I did for the return).
I've rented a car, used the Magical Express, and the Blue Van.
Used Magical Express a month ago as a matter of fact from John Wayne.
It is cheaper, and leaves at regular intervals.
Blue Van leaves when you are ready, but costs more. I used that from John Wayne.
Last time I rented a car, it was from LAX, and it was when the Disneyland hotel offered free self parking. It was slightly more expensive, and we only used the car to get to Disneyland, and go back to LAX, it sat unused the rest of the time.
I have also used a one way rental car from LAX to Anaheim (National Rental Car--it's on Katella AVe near DL). I was able to get a good price for a 1 day rental. There were 2 of us and we wanted to make a couple of stops on the way so it made sense.
On that trip we went back to the airport on different days, so DS used the Disney Resort bus and I used the Super Shuttle. I believe the Disney Resort Bus costs a bit more (it looks like $30 OW or $48 RT) than the super shuttle and it runs on a scheduled departure time.
I did this way back when. Not the most pleasant way, but you get there pretty directly, actually.
Go to Google maps and search for directions from Los Angeles International Airport World Way to disneyland harbor boulevard. Takes about two hours.
Anything else is way more. One thing to consider, if you do the super shuttle or something like it, you have to times the $20-ish fare by as many people are going and that adds up. If you have a few people, then car rental looks more attractive