Tankless heaters score higher environmentally in other ways. Whereas tanked heaters end up in the landfill, tankless heaters are made of recyclable (metal) parts. They are also repairable, and manufactures claim they last at least 20 years (much longer than tanks); Bosch warranties the heat exchanger on our model for 15 years.
Tankless water heaters complement solar hot water nicely, since they cost nothing to operate when they're not in use. Our model doesn't support solar hot water, and I somewhat regret not purchasing a model that does, just to leave the option open.
On the downside, tankless heaters initially cost more (in 2003, $1000 to $1500 vs. $400 to $1000, installed), though they more than pay for themselves by using less energy and lasting longer. The higher price includes the common one-time expense of relocating the heater, $500, so the next one will pay for itself even faster.
A tankless water heater could require some changes in your hot water consumption habits.
Smaller heaters like our model can only supply enough hot water to supply one major thing at a time. This hasn't been an issue at all for our family of three, but if you have a larger family and need to have several things running at once, you'd need a bigger one.
Also, since our unit has no pilot (it uses electronic ignition to save energy), it takes about four additional seconds -- beyond the normal delay of moving water from the heater to the faucet -- for the unit to begin to heat the water. So when you want to wash your hands with warm water, you'll have to wait the extra seconds before the hot water arrives. If someone comes along five minutes later to wash, they'll get the leftover hot water in the pipe, and then cooler water from when the heater was turning on again. So guess what? We gave up and just wash with cold water. Models with a pilot probably don't have this problem, but consume a bit more gas.