We ALWAYS rent a car and use it for virtually all of our transportation. Rarely do we use Disney transportation. I don't think Disney transportation is bad--it's quite good for what it is--it's just not our preference for a number of reasons. Yes, we do like to save time, and no, that isn't a moot point to us. Our vacation time is short and precious and we'd prefer to spend it having fun with each other, or standing in line for a great ride, not a bus. I do the majority of our vacation driving and I don't mind it. In fact, I enjoy it - it feels like driving around our "other hometown." Here are some thoughts on the pros and cons. (Pros are first, in case you can't tell.

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-Everyone always has a seat.
You can't say the same for buses, which are often crowded at park opening and closing times. Yes, if a bus is SRO, a person can choose to wait - but the option of standing and waiting for yet another bus (who knows how long that will take) isn't exactly appealing, either.
(Incidentally, as someone above said, yes you do have to fold your stroller to use your car, too - but in your car, you have somewhere to put the stroller. Not so on the bus.)
-My rental car goes exactly where I want to go.
After leaving Animal Kingdom, my son often wants to stop at McDonald's for a cheeseburger (one of his favorite things). In my own car, I can do that - no so for a Disney bus.
-I come and go on my schedule.
I don't wait for a bus to arrive. I don't wonder how long it's going to take.
-I never worry about making it to my resort restaurant ADRs.
Sorry, but using personal transportation from resort to resort IS a big time savings - a little extra rest time or time to get ready for a nice dinner out, or on the return "home" it means a little more time for an evening swim or our family tradition of playing a game. No leaving 60-90 minutes ahead of time to make it using WDW transportation.
-It's private.
No listening to other people argue or talk loudly on their cell phones. We can have private conversation. Our car can provide a bit of refuge from over-stimulation. This may seem trivial to some, but having a son with Asperger Syndrome, it's a big deal to us.
There are many more IMO- you can go offsite to other attractions, to other restaurants (like Chick-Fil-A, which I can't get at home!) or simply get your own groceries.
Some cons:
-It is an additional expense.
-Some people may not be comfortable with directions or finding their way around.
-You don't get dropped off at the park entrance.
-...
Okay, so I can't think of anymore cons.
