Future of Tire technology
I'm not sure you know what tubular tires are (they are relatively rare), but I'll describe the 3 basic tire systems for bicycles:

The most common is the good old clincher tire.



(Image from Wikipedia: Bicycle Tire)

The tire (4=bead,6=casing,7=tread) hooks into the rim (1) via the bead (4). The air is held through an inner tube (5) which is protected from the spoke nipples by a rim strip (2).

Theres a lot of reasons for using this:


If you have a flat, you can easily swap the tube and/or tire, no mess required. 
Tubes are repairable. Tires sometimes repairable. 
Everyone knows how to deal with them and stocks them. 
The rim doesn't have to be anything special. 
Cheap, cause everyone's been using them forever. 


However, there are some disadvantages:


Tubes do have some weight to them.
At low pressures, you can pinch the tube and get a flat.


A tubular tire is basically a tube wrapped in the casing and then glued onto the rim. A picture is given below:

(From this question)

According to Sheldon Brown:


Lighter tires and rims than similar clinchers
Less likely to pinch flat
But on the other hand,
Hard to repair
Expensive
Can roll off the rim if you don't glue them properly 
Higher rolling resistance
Not always as round/true as a clincher.
Rare -- pretty much only certain racers use them (road, cyclocross). 


Finally, we come to tubeless. The mounting system is the same as whats given for the clincher tire, except you don't have an inner tube (5) or rim tape necessarily (2) [Depending on the rim, you may need some tape to make it airtight]. We can distinguish between tubeless rims+tires and tubeless-ready rims+tires (the latter requiring using a liquid sealant with the tire+rim in order to seal the tire, while the former it is optional). 

The good things are:


You can run lower pressures since theres no tube to flat (better traction)
Lower rolling resistance 
The sealant provides some puncture protection for sealing


The bad is:


Installing the tire is a lot longer than a tubed tire (Schwalbe notes that it may take up to 3 days for the sealant to seal the tire)
Messier to replace a tire since you have to clean out the sealant
You may need to carry around a spare tube anyway, if something happens to stick in the tire and keep moving. 


One may argue that tubeless are lighter or heavier than clinchers, but that depends on the system of tubeless tire, so I've left that out. 

These things are primarily advantageous for mountain bikers. For road bikers, not so much. 

The big reason why I think a lot of people still ride clincher tires is cause they're easy to maintain, cheap, and everybody knows how to deal with them and has the parts. Mountain bikers see real advantages with tubeless, while road bikers don't really see advantages, so they do ride tubeless fairly often, but still, the tube is not leaving us any time soon.