DOHC, SOHC, OHV valvetrains, whats the difference

First off, DOHC stands for Dual-OverHead Camshaft, meaning that each bank of cylinders has two camshafts controlling the valves. For an inline engine (virtually all 4-cylinders), which has one bank of cylinders lined up, this means 2 camshafts total. For a V-style engine (V6, V8, V10) this means 4 total camshafts, as each head gets their own double camshafts. By having two camshafts per head, each camshaft is dedicated only to the intake valves or the exhaust valves, not both, and because of this, they can be located directly above the valve. 

By having the camshaft directly above the valve, it eliminates the need for rocker arms that are required in non-DOHC designs, and thus has fewer moving parts. Because of this, DOHC engines generally can rev higher than other engines as they have less valve train inertia, although the actual difference is not tremendously important in non-racing engines

 DOHC engines lead to easier implementation of multivalve engines, as they don't require rocker arms and other supporting hardware for each valve, thus allowing for easier and more efficient breathing of the engine. 

The bad thing about DOHC engines is that they are very large and bulky given their displacement and they are expensive. Having 4 camshafts adds a lot of space in the heads and makes the engine take up much more room than other engines. For example, the Chevy Corvette motor takes up less space than a Cadillac Northstar engine, even though the Corvette's engine displaces six liters and the Caddy only displaces 4.6. Having additional camshafts also makes the engine much pricier and requires the use of a long timing chain or belt. 

SOHC (single overhead camshaft) engines are similar to DOHC engines except they have one camshaft per head (so one camshaft total for an inline engine, two total for a V-style engine). This splits the benefits and problems inherent with DOHC designs - they require less space because they have half as many camshafts, but have additional mechanical complexity because it is impossible to locate one camshaft directly above both intake and exhaust valves, thus requiring hardware to translate the camshaft's movement into moving each valve. This additional machinery adds valve train inertia. SOHC engines also require a long timing chain or belt. 

OHV (overhead valve or pushrod) engines are on the other end of the spectrum from DOHC in that they are the simplest, lightest, and least expensive design used in current vehicles. In these engines, there is always only one camshaft, regardless of configuration. Virtually all modern OHV engines are V-style (with the exception being the Cummins Turbodiesel, which is an inline-six). The camshaft is located directly in the middle of the engine, in the block, in between both banks of cylinders, and actuates the valves with long metal rods called pushrods. This leads to multiple effects: 

- OHV engines have simple engine heads, as they do not contain camshafts and only have the rocker arms; 

- OHV engine heads are much smaller than other designs, leading to increased space efficiency; 

- OHV engines generally cannot rev as high as other designs because the pushrod adds valvetrain inertia; 

- OHV engines have timing chains that are generally permanent. 

It is much easier to implement cylinder shutoff technology (such as GM's Active Fuel Management, or Chrysler's MDS) as well as variable valve timing in OHV engines. As an example, GM added variable valve timing to their 3.5 liter V6 with little more than a camshaft phasor, which is a simple and inexpensive device, and yielded over a 10% increase in horsepower with no difference in torque or fuel economy. A caveat is that variable valve timing can never be as sophisticated with only a single camshaft because the intake and exhaust timing cannot be changed independantly of each other. 

One common issue that is often brought up about OHV engines is that they are unable to rev freely. 

Honda currently is the main user of SOHC engines and they make great powerplants. Most other producers use DOHC designs and these are good motors too. But here are a few vehicles, and while there are tons of other factors such as transmission options, this can give you an idea: 

OHV 

GM 6.0 liter V8 "LS2"      400 hp/400 ft-lb  18/28 mpg 

GM 7.0 liter V8 "LS7"      505 hp/470 ft-lb  16/26 mpg 

GM 3500 V6 "LZ4"        224 hp/220 ft-lb  22/32 mpg 

DCX 5.7 liter V8 "Hemi"    340 hp/390 ft-lb   17/25 mpg 

Ford 3.0 V6 "Vulcan"      154 hp/180 ft-lb   18/27 mpg 

SOHC 

Honda 3.0 V6            244 hp/211 ft-lb    21/30 mpg 

DOHC 

Toyota 3.0 V6          190 hp/205 ft-lb     20/29 mpg 

Toyota 3.5 V6          267 hp/244 ft-lb     21/31 mpg 

GM 3.6 V6 "HF"       255 hp/252 ft-lb     20/28 mpg