Gardeners generally have it easy in this area, at least. It wouldn't be fair to say there's no stress in the gardening trade—overbearing bosses exist in every industry, and other day-to-day stressors always find a way to creep in—but there's not nearly as much as in other lines of work. This ain't brain surgery, it's just lawn surgery.
Most stress does not come from the work directly but rather from rushing about town to get to various jobs in a hurry. Usually they'll need to retrieve tools and a vehicle from the company yard, then travel miles to the jobs they have on their slate.
No client is going to pay their gardener for the time it takes to get there, so that driving adds up to a lot of time that could otherwise be spent making more money. Remember that speeding is a bad way to try to make that up.
If you're on the management end of things, the stress is like that of running any other business: when you're not making money, it's stressful; when you are making money, it's much less stressful.
But even with the added book-balancing stress, it's good to be the boss and send out a whole bunch of people-who-aren't-you when it's 110 degrees outside with no breeze and no shade in sight. On the other hand, that kind of heat also means added stress if you're just another one of the crew members.
Speaking of the heat, awful weather can be a bit stressful if no work can be done outside. And beyond being subject to the whims of Mother Nature, there's also the clientele to worry about—you may even have an altercation or two with clients (people can get pretty fussy about the way their shrubberies are arranged).
Landscapers who do a good job shouldn't have too many unhappy clients to deal with, so just keep those headphones blasting some good beats while you're working and your day should be fairly stress-free.