What kind of plant did EVE find?

My guess is that it was intended to be an apple seedling. I regret, however, I have no strong evidence for this - just lots of suggestive hints.

For a start, the sapling looks like a CG apple seedling (but note my edit at the bottom about this):

The Wall•E sapling.

A CG Apple sapling.

Even the EVE project logo, which I feel is a foreshadowing/echo of the seedling she finds, looks like an apple tree logo.

The EVE seedling logo.

An apple tree logo.

But also, consider the obvious Adam/Eve symbology here.

What plant would EVE find, but the apple tree? Metaphorically, it fits: she finds the tree of knowledge that leads humanity away from the Eden of perfect bliss to the deeper life of hardship and knowledge.

But perhaps most significantly, I think, there's another angle. EVE was a love letter to Apple, the company.

Andrew Stanton, Wall•E's director, said "The more I started describing [EVE's design], the more I realized I was pretty much describing the Apple playbook for design." So he called up Steve Jobs, who sent his lead designer, Jonathan Ive, designer of the iMac, iPhone, iPod etc, over to Pixar to consult with Stanton on the prototype. http://www.firstshowing.net/2008/apples-designer-actually-helped-design-wall-es-eve-robot/

Pixar used to be owned by Steve Jobs, until Disney bought it.

The movie features a video iPod (Wall•E watches "Hello Dolly!" on it; the Mac Welcome chime (when Wall•E finishes recharging); Apple mice skitter across the floor; there's a Mac keyboard in Wall•E's truck; the spaceship's computer control speaks with the voice of the early Mac speech synth, "MacinTalk"; and so forth.

Did EVE definitively find an apple? I don't think so. But I don't think any other plant makes sense.

[Edit: all the above said, my impression from the movie was that it was some kind of vine - or a beanstalk? A jack-and-the-beanstalk reference, perhaps? @Valorum makes a good point in their answer that this is provably false given the final credits animation shows it to be a tree sapling, and I think also makes a good, script-referenced argument that the plant is deliberately ambiguous. Oh, and the concept art links of a "pea plant" is essentially identical in shape and even angle to the sapling in Wall•E's hands in the screen shot I link to, so I'd argue that is what it was designed as, even if not what it was intended to be.]

My guess is that it's just a "generic" plant, used by the animators to symbolize the natural world.

That said, I count at least three distinct leaf types in the concept art drawing, each coming from a different type of plant, so it might be a hybrid that was genetically engineered to produce multiple products on the same stem (strawberries on this branch, raspberries on that one, etc.).

The bottom leaf looks like a type of Ground Ivy, which is fairly common where I live. I don't know the others off-hand, but this chart should help identify them.

Hope this helps!