In areas of the world where temperatures are documented to be growing warmer, plants are showing the effects. Some of these effects are good – increased microbial action in the soil making plants more productive. Some are bad – plants moving to cooler locations.
And other effects tend to be neutral (or maybe it's who's doing the perceiving).
Gardeners, for instance, often long for plants that grow only in climates that have typically had winter weather warmer than their own. But now they're finding that many plants are making themselves at home where they wouldn't grow before. ( This article in USA Today discusses it in more detail.)
The downside of that is, potentially: Plants that are currently a big part of a particular climate -- sugar maple trees in New England, for instance -- will be sorely missed if they migrate northward.
Warmer temperatures – say, 3 degrees C warmer – and stronger winds (which are considered part of global warming) actually quicken the spread of seeds, pollen, and plants, noted Science Daily earlier this month. This could help plants survive and be useful in repopulating forests that have been leveled by fire.
The plants best suited to move easily into a new climate zone tend to be those that live on the edge of their current zone, said researchers in a study published in the journal New Phytologist.
Less snow cover – which keeps soil temperatures steady – would lead to more thawing and refreezing of soil, which adversely affects roots of many plants. However, reports TreeHugger, this heaving action "increases microbial action and breaks up the soil, make plants more productive."
We've written previously about possible changes to various weeds due to climate change. A study reported in January noted that if higher temperatures cause invasive plants to move to areas with warmer temperatures (and some invasive plants could become less competitive than they are now, researchers found), this will provide space for welcome restoration of their current acreage.
On the food front: A couple of days ago, in an article titled Crops face toxic timebomb in warmer world: study, Reuters noted research findings that tested several food crops such as cassava and sorghum – which are staples in Africa, Asia, and Latin America – to see how they reacted to elevated CO2 levels.
One result: At double the current rates of Co2, the plants produced much higher levels of chemicals that break down in cyanide gas if chewed or crushed and much lower levels of protein. (The protein is necessary for people and cattle to break down the cyanide so it has no effect on them.)
Some other reports you might be interested in:
[Added later:] Why Invasive Plants Take Over
Hooray for Global Warming! 
All in all, the answer to our question is: It's a mixed bag. Stay tuned for more research – and real-life experience.