Why buy an new plane or an helicopter?
Because some people like new things... Thats how salesmen stay in business. 

There are however some practical aspects to this question and on the tail end of my instrument rating I've been getting serious about buying something, here is what I have found. For the purposes of this answer I'm only going to talk about aircraft that are still in production like the 172 and have been for some time. The only other comparable aircraft is the Piper Archer. Mooney no longer makes the lower power stuff, the early low power PA-28 variants have been out of production for some time and are thus out of scope. In the end it depend s on what you, the pilot/owner/operator really wants out of the aircraft. 


While a 1956 172 will share a lot in common with ones rolling off the line now a G1000 cockpit is not a steam gauge cockpit. A G1000 unit, or any of the various glass options for retrofit are NOT cheap to buy and install. Thus if you get a decent, low time 172SP and replace the panel to make it just like a new one, you have already spend about what a new one costs and there may very well be 2000 hours on the airframe already. 
The older the plane (generally), the more engines its been through. A well flown early era 172 may very well be on its 2nd, 3rd or 4th engine. These engines could have been overhauled, rebuilt, swapped by various different entities in various ways. There may or may not be a warranty on them anymore and you may have little protection against it blowing out on you. Meanwhile a new plane may come with a warranty which represents real tangible value especially considering the first hundred hours or so of an engines life are quite critical. You can find all of Textron/Cessna warranty info here. 
You are buying effectively a 0 time engine (or as low as practical) again you can buy a nice 172 then go spend another 20K, 30K, 40K... putting a fresh engine in it to get a "new" airplane. 
The paint and interior are new and clean. There is nothing quite like the tired velour interiors of rental aircraft but even second hand planes often have tired 80's fabric that have seen a lot in their time. A fresh paint job and new interior is not cheap, especially when you realize you need fireproof fabric, may need to take a lot of the plane apart to paint it and dealing with the downtime. We come back to the 80's 172 that needs paint and a costly interior example... 
Finally, old planes are just tired. Even planes that look to be in good shape, pass inspections, and fly great dont last forever. Some times you are just taxing along and your gear gives out...  


Buying an old plane and making it a new plane may just cost as much as a new plane.