I specify the difference between dinosaurs and other forms because in many cases, dinosaur Wild Shape forms are in a whole different league-- I for one don't like them, because visually it creates a very different kind of game.
If you don't mind that, or like the idea of becoming one, then the deinonychus is easily your best bet for high DPR. Four natural attacks per round (the most of any Medium-sized animal), two of them d8's, and pounce to boot. A 60-ft movement speed makes it the fastest land animal (sorry, cheetahs, Wild Shape doesn't grant you the sprint ability of pure-blood cats), so you'll almost always be the first in the party to make a full-round attack and maximize your damage output.
Everything else: Leopard
Like many other Medium-sized animals, a leopard has three natural attacks per round-- but unlike those other chumps, it also has pounce and rake. Cheetahs get trip, dire badgers get a burrow speed and ferocity, but only leopards can make all of their attacks in the first round. (You can even add your two rake attacks on a pounce, for a total of five attack rolls-- unfortunately, it's not something you can do every turn.) It only has a 30-ft movement speed, which isn't great, but it also has a 20-foot climb speed if you need it.
Note: For very long combats, there's another form that actually edges out the leopard-- the wolverine. It has two d6 claws and a d4 bite, but doesn't have pounce. If a leopard druid and a wolverine druid each go toe-to-toe with a training dummy, the wolverine eventually wins on damage output... on round 9. Most fights won't last that long, so the leopard is still the better choice, but it's worth mentioning.
Honorable mention: Giant Porcupine
Giant porcupines have the distinction of having the highest-damaging natural attack of their size-- a 2d6 tail slap. (Sadly, Wild Shape will never grant you full use of those quills-- but giant porcupines can't use them offensively anyway.) So if you still want to pull Vital Strike shenanigans in a 5-ft corridor, this is the form for you.
What about elementals and plants?
An earth elemental might look tempting because of that +4 Str bonus, but remember that it only gives you a single d8 slam every round. So while it might be a strong contender for Vital Strike tactics (you'll hit more often as an earth elemental than as a giant porcupine, and for almost the same damage), from a total DPR standpoint it's not a good option.
Admittedly I'm not very familiar with plant shapes, but I doubt there are any Medium plants that can compete for damage. Plants tend to have slow movement speeds and only one or two (usually weak) attacks, which are both bad for business. Where they excel is poison and other debuffs, which are a great thing but a different thing.
There is one huge exception to this: a Green Man. Technically a Medium plant, by RAW a Green Man is a legal Wild Shape option (as far as I know). You won't get any of his coolest abilities-- greensight, lifesense, spells, etc.-- but you'd get a whole slew of amazing natural attacks from being one. A Green Man is essentially a living god, who can grant spells and everything; expect your GM to give you a hard no on this.