**1)** [*Rhizopus stolonifer*](https://en.wikipedia.org/wiki/Black_bread_mold
), also known as the black bread mould, is one species amongst a small group of mould fungi that can parasitise both plants and animals. You've almost certainly seen it growing on old bits of bread and other foodstuffs you've forgotten about at the back of the refrigerator n' cupboard. Alongside growing on decaying food, it can also infect the tissues of living plants, and occasionally animals such as ourselves, causing [zygomycosis](https://en.wikipedia.org/wiki/Zygomycosis
). This can be fatal.
**2)** Cancer is also a disease universal to all multicellular life, though cancer in plants acts in a *totally different* way to that in animals and it doesn't *particularly* harm them.
For background; cancer is basically a population of cells that's mutated in such a way that they've overcome the natural control on cell division and multiply uncontrollably. In animals, they divide, within fairly malleable tissue compared to plants, to such an extent the tumour eventually breaks through into the vascular system, at which point the cancer cells hitch a lift around the body in your blood, forming daughter tumours pretty much everywhere (known as metastasis) and, well, things aren't so peachy.
Plants lack an equivalent vascular system - the xylem and phloem they use to transport water and nutrients through their stems cannot pass large cells (plus, plant cells are rigid in structure, so couldn't get into them anyway). So cancer cells in plants - which crop up at a lower rate anyway compared to animals due to their low metabolic rates amongst other things - are stuck where they began, and only grow locally.
It's actually exceedingly common. If you look at any old tree, you'll notice a whole loada' lumpy galls n' burls - [these are tumours](https://uconnladybug.files.wordpress.com/2011/04/dsc02076.jpg
). Indeed, some animals even take advantage of how tumours develop in plants to induce them on purpose for various reasons, such as gall wasps who induce 'em to provide shelter for their growing larvae.
So yup, cancer in plants, particularly long-lived trees, is common but by no means much of a burden on their system and so they can proverbially shrug it off to a large extent.
Erm, but anyway, aside from cancer and the odd opportunistic fungus, I can't think of anything else!
[^(Sablowski, R. & Doonan, J.H. (2010)^) ^(Walls around tumours — why plants do not develop cancer. *Nature Reviews Cancer*. 10, 794–802)](https://www.nature.com/articles/nrc2942
[^(Gaspar, T. (1998)^) ^(Plants can get cancer. *Plant Physiology and Biochemistry*. 36 (3)^) ^203-204](http://www.sciencedirect.com/science/article/pii/S0981942897868763
One controversial idea in my field: whether prions (infectious proteins) are taken up by plants, where they may be harbored and concentrated before later being consumed by the mammalian host, transmitting the agent.
The plants aren't specifically *affected* though they could still be considered *infected* with the prion.
[There are quite a few pathogens](http://onlinelibrary.wiley.com/doi/10.1111/j.1574-6976.2007.00065.x/full
), scroll to Table 1.
The short answer is yes, but a typical plant pathogen infecting humans is not that common, because pathogens usually establish a niche in a host where they like to live. Unless there is a good reason, like loss of its habitat/environment, pressure from a toxin/chemical, opportunity in a human host, plant pathogens usually like to stay with their niche host.
edit: grammar and typos
*Burkholderia pseudomallei*, *Pseudomonas aeruginosa* several other of the Burkholderiales and Pseudomonads and a lot of other opportunistic pathogens that make their home in environmental niches that mimic a niche in a mammalian or animal host. Interestingly, there is a theory that these pathogens are pathogenic to humans and other higher order organisms because some of their natural predators are ameobae which share some innate immune mechanisms with higher order organisms - i.e. they "train" in free living amoebae and can then infect animals.