I'm going to harp on a bit now about cabs because I use them frequently when in Orlando as I've always visited as a non-driver.
Checker Cabs, Yellow Cabs and City Cabs (there's another as well but I can't quite remember it at the moment) are all part of the MEARS Group. These are the cabs that will have the (407) 870 -0000 number for Kissimmee/Osceola or the (407) 699-9999 number for Orlando/Orange Co. If you ring these numbers you will be sent any of the above cars come to pick you up - if you specifically want say a "Checker" or "City" cab to pick you up you need to specify when making the booking all of which takes less than a minute. I've never waited more than 5 minutes for a cab to pick me up.
On WDW property, Checker Cabs are however the only ones that can take you through the admission gates without having to pay the car park fee and therefore pass that cost onto you, the passenger. Also if you are staying on property (except at the Swan or Dolphin) when you ask the valet or bell services to call you a cab it will be a Checker that comes to pick you up if there isn't already one just hanging by the hotel, which WDW have given approval of and that is as good as an endorsement as any.
At the Swan and Dolphin if you ask the valet for a cab you will be directed to one of the white town cars that are lined up by the front entrance. These are non-metered white town cars and it would be my impression that they either work for S & D or they pay something to them. The above mentioned cabs that are part of MEARS are not allowed to stand on rank at either the Swan and Dolphin. If you take one of the white town cars cars from the S & D your fare will not be metered so you need to ask them how much before you take the ride. One charged me $16 to AKL and another once charged me $20 so you see it differs. LOL I don't know what it costs in a metered cab as I've never got one from there. But I also got one from the Swan to The Poly (further than the AKL) and that cost me $20 as well so I figured I either got a bargain to the Poly or got stitched up at AKL

These town cars are very professionally run but if you do stay at the S & D and want a metered cab from the MEARS group you can call for one from your hotel room or payphone in the lobby and one will come and get you because it is a pre-arranged fare.
I think we may be the friends that Deb is referring to who got lost from our Disney resort by Epcot and yeah he missed the turning and so we kept driving and driving (he was a Checker cab that works mostly I-Drive and WDW) but we were chatting about all of these restaurants so I sort of felt responsible for his lack of concentration but he then realised and turned around and took the money off at the end which we thought was very honest of him. So even though we gave him $30 he was only going to charge us $26 the meter read something like $38 and our hotel had quoted us $45. LOL it was our own fault as when we rang him to take the fare (he'd taken us to Florida Mall a couple of days before and given us his card) he told us then he didn't know where it was and by the time he came to meet us he had asked others too but in the end he used his own cell phone to ring up Deb and ask for directions we thought that was really sweet of him and we would use him again just not to a private villa address
Now what you do need to BEWARE of are what the industry know as "GYPSY" cabs - these drivers cleverly disguise their cars by spraying them yellow and therefore you may immediately think it's a safe cab run by the MEARS group or perhaps you think they are from another reputable company just because they are on Disney property. Please check that these cabs are insured those from reputable companies are insured should anything happen to you whilst you are in the cab and I believe that this information is on display somewhere in the cab. The "GYPSY" cabs tend to hang around Downtown Disney so please also look for the phone number on the side of the cab and check that it is one you recognise before getting in. The drivers I.D should also be on display. Another way to tell is if they have there rates displayed on the window or inside the car.
Town & Country are another taxi company who have the rank at Florida Mall, therefore unless you specifically ask for another cab to come and get you they won't be hanging around so if you don't want to call a cab and are in a hurry you'd have to get in the T&C cab. They are regulated but tend to work with the meter off. You can ask for the meter to be put on but remember if you start sitting in traffic that will mount up but if you sort of know what the fare is supposed to be again you need to get your price before you take the cab. EPCOT to Florida Mall runs around approx $30 to $35
I have taken about 50 odd cabs from WDW or I-Drive areas from the MEARS group mainly and they have always have gotten me to the place I wanna be bar the Villa incident.
Please remember that you do not have to take the first cab offered to you. If you think the driver behind, the one that draws up to the side of you, is the one that's gonna get you there or you feel safer with then take it, doesn't matter what anyone tells (or shouts at) you it's your call.
Shuttles are OK but I just prefer (and don't mind paying) for the freedom of a cab that is a) either already waiting on rank or b) comes to get me when I want it to and if there is more than 4 of you a Cab is often cheaper than 4 fares on a Shuttle. This is just my opinion.
I know I've gone on a lot but I just wanted to give a bit of a perspective on how the Taxi industry in the Orlando area is run.