Limousine, carriage, bus, car, van, tractor, horse... you're going to need transportation. (Unless the party is at your place.)
Some wedding dresses are not conducive to driving yourself. If you plan to do it, I urge you to try it out beforehand. Wedding days should not include a mishap where the bride’s gown gets caught under the gas pedal.
Consider how much transportation you need and when. There’s travel from wherever the bride and her party gets ready, and travel from wherever the groom and his party gets ready—to the ceremony location. Then there’s the ceremony, which might last up to three hours (depending on what you have planned). Next up is usually pictures, some of which will probably be at your ceremony site, and some which will require the party to visit another, more scenic, location. Then it’s usually on to the reception hall. Factor in at least five hours. Now everyone needs to get home. There may be various levels of sobriety to consider.
Limousine companies may charge by the hour, which can make this an impractical option. Research is needed to get the best deal. Generally, unless you ““know a guy”” this is just an outrageous expense.
A horse and carriage is slower than many people realize. (Unless you have grown up using this mode of transportation, and thus are familiar with the pace.) If your wedding ceremony is indoors, the carriage rolls up and no one even sees it. (Except for the photographer, if you’ve alerted him/her.) There’s also the weather to consider, because rain will be far worse in an open carriage. And the wind can do a number on your hair. Cinderella had a hair and make-up team, and plenty of movie studio people to fix strays and snags. If your heart is set on this option, it’s fine, just know what you are committing to. Preparedness is the key to preventing most disasters.
Elephants will almost certainly require a permit. Be sure to check the laws and ordinances of your area before planning any non-motor-vehicle transportation. Also find out if your wedding procession is allowed to run lights and stop signs to keep in line. (Very rare.)
A popular money saving-option is to ask a few friends or family to serve as drivers. The cars are decorated (don’t ruin the paint, don’t ruin the paint, don’t ruin the paint), and these loyal people are devoted to hauling your party around all day. Select those who are okay with being designated sober drivers (if you’re serving alcohol).
If you can find a unicorn to serve as transportation, you should definitely do that. ;)
If you get the Chicago PD to drive you, you might be in the movie My Big Fat Greek Wedding 2.