I don't necessarily have the tools or experience to try to build some big fancy box, and everybody that I know only go either ported or sealed. I don't really know of which other options there are...
sealed is the smallest. easiest. and does lots of things right. but you need twice the number of subs to equal the output of a ported box.
ported. well this is what you see the most of. they get loud, are the second easiest box type to build and design. done right they sound good. bigger than a sealed box.
4 th order band pass, sealed and ported boxes with a sub in the middle. can be tuned for spl or sq. MUST be designed for one model of sub. (no off the shelf will be good examples of this type.) Normally slightly larger than a ported box. Fr is made for sq is closer to a sealed box. But loud as a ported box. lpf and ssf are not needed if designed correctly.
6th order bp. same as above but both boxes are ported.
Transmission line (TL) just search for it. Sounds great. normally bigger than a ported or band pass box. works differently than everything listed above.
horns, you have seen these right? very efficient, huge when used for subs. true horns are not used in cars much do to size.
tapped horns, puts the driver in the mouth of the horn, allows for a smaller horn, some times used in cars.
IB - like sealed but with a huge box. (ie the box is the trunk.) sq only, low power handling, need big subs and often eq
I'm sure I missed some. I got tired of typing on my phone, Google for more details I'm any of the types of boxes