There are many types of tourism, below is meant to provide some coverage of the totality of topics:
Also Extreme Tourism, for the more dangerous/exotic kinds of Adventure http://en.wikipedia.org/wiki/Extreme_tourism
Tourists being involved in agriculture in some way, picking berries, making wine, dude ranches, etc.
Air Travel and Air Tourism
Including ballooning, and other kinds of flight (hang gliding up to jets), for example small plane flights over the Grand Canyon, seaplane flights over San Francisco bay, etc.
Amusement Park Tourism
This could be caring for, studying, or hunting, killing, and/or eating animals (or really, any living thing).
Places to star-gaze, witness eclipses, meteor showers, and things like the aurora borealis.
Travel to significant sites in atomic history such as museums with atomic weapons, vehicles that carried atomic weapons or sites where atomic weapons were detonated. - Atomic Tourism - Wikipedia
Tourism by bicycle, can be long journeys or things like road biking, or even urban bicycle tourism.
Small or large ships, can include sailboats. River cruises as well as large luxury ocean-going cruises.
Cultural experiences or performances, high culture or slum culture.
Dark Tourism, aka Atrocity Tourism
Places associated with death and suffering, though there may be a cathartic effect, as in Can Dark Tourism Help Cambodia Heal?
Where death took place or even where one wants to go to die
Places where great disasters have happened, including volcanos, meteor impacts, nuclear disasters (Chernobyl, see the amazing stories and photos of Chernobyl by Kid of Speed)
Visiting sites/phenomena that will be gone soon: Ice caps of Kilimanjaro, coral of the Great Barrier Reef
Going places to get high or experience the local drugs
Ecologically low footprint but also the ecology as the object/destination of the tourism
Touring in a place to gain educational experiences or credits (or degrees), including various aspects of study abroad.
Fertility, Reproductive, Maternity, and Birth Tourism
Travel to other countries in order to reproduce (for biological or legal reasons), https://en.wikipedia.org/wiki/Birth_tourism
See also agritourism. This can be anything from street food to Michelin star dining.
Gap Year Tourism
Gap Year is an Aus/NZ item where a year is taken between school and work, or between school and school
Check out gardens, apparently all the rage in Europe and the UK in the 18-19th century.
Finding relatives, grave markers, etc.
Coined phrase incorporating a variety of sustainable, built-environment elements
Historically prominent sites to see, such as the Taj Mahal, etc.
Health food, spa, yoga retreat, fitness camps, etc.
Can be sex tourism or just gay friendly
Cosmetic surgery (ศัลยกรรมเสริมความงาม), routine surgery, rehabilitation, dental work, etc.
MICE (Meetings, Incentives, Conventions, Exhibitions)
Also called business tourism
Mountaineering, Trekking, Mountain Climbing
Going places to hear music (e.g., larger concert events in different places) or to learn or play music, or even record music
Nature Park Tourism
Sailing and Boating (overlap with Cruises above)
Touring to or between large parties or events, such as the Full Moon party
Pop Culture Tourism
Travel to religious places or events, pilgrimages; aka sacred tourism, and pilgrimages.
Similar to Sustainable, usually minimizing impact on animals and people economically and culturally
Seasonal (yearly migrations) as well as expatriation, though it is a question when Tourism ends (e.g., for the Digital Nomad)
See Wildlife Tourism
See also Metropolitan tourism
Including space station, lunar, and (hopefully) interstellar tourism.
Participating in marathons, Muay Thai camps, to spectator sports Olympics, etc., see also Snow Sports and Water Sports Tourism
Spring Break Tourism
Go somewhere to get drunk for a week, see also drug tourism
Travel to other places to kill oneself
Can be carbon neutral, or other ways of measuring sustainability
Surely a possibility
Train hopping, train hitching, hoboing
Usually in archeologically significant cities
Virtual experience of tourism
Tourism around work, possibly skill updates, professional development, etc.
Volunteering and tourism combined. Includes the rather disturbing orphanage tourism
Tourism near or in a war zone
Water Sports Tourism
Snorkeling, Scuba Diving, Free Diving, Fishing
Anything from birdwatching, butterflies to safaris
Aka Enotourism, can be a part of party tourism, food/culinary tourism, agritourism. Similar to this is Distillery tourism (Scotland/Ireland).