As you can expect there are many good transport companies so it depends
on your budget (and size of your party?).
Uber - can pick you at Animal Kingdom and is growing in popularity - but it is a long way for them however.
Cheapest - To do it really cheap you can take the Magical Express early to the airport then hop on a shared shuttle bus (same size as the
DCL bus) for as little as $14.50 per person (see goportcanaveral below)!
Cost-effective- You can also rent a car one-way.
Others -
who are mentioned often and positively:
Cocoa Beach Shuttle – based near Port Canaveral. The “go to” shuttle for many cruisers. Also offer scheduled shared shuttles. Preferred by many Canaveral hotels for port and airport transfers.
Happy Hour Shuttle – based near Port Canaveral. Small local company slowly building a solid reputation.
Executive VIP Limousine – based near Port Canaveral. Many good reviews on the internet.
Happy Limousine – Recommended by some Disney travel agencies.
Orlando Chauffeured Services – Based in Orlando, Good reviews on the internet.
Mears Shuttle – With a desk at Orlando Airport ensuring personal service. Operates the Disney and Carnival transfer buses.
Groundlink – A nation-wide value-add service trusted by many travelers. Also has exclusive agreements with some cruise lines. Often more expensive but you can trust the service.
Travelynx Stylus – A large company with a good reputation. The preferred transfer company for many Canaveral hotels. Parent company is based in Orlando.
888-Transportation – based in Cape Canaveral with an exclusive agreement with Port Canaveral, allowing hail services. They have taxis waiting at the cruise terminals. Call ahead to ask about shared shuttles from the airport ($25 per person) or private shuttles for $90 (up to 5 persons). Also from the resorts.
Cortrans Shuttle – Consistently one of the cheaper shuttles with good reviews. Also offer scheduled shared shuttles. Based in Orlando.
AA Access Transport – One of the most popular shuttles with shared scheduled services and vans of all sizes. Based in Orlando.
Goportcanaveral – A local
travel agency with really low cost transfer and hotel packages. Some of their rates are the lowest available. Based near Port Canaveral.
FL Tours – Recommended by several Disney Travel Agencies. Based in Orlando