Itch and irritation is caused by brushing against a common plant, like poison ivy. 
But there are many other plants that can cause contact dermatitis — skin inflammation cause by an irritant or a substance that produces an allergic reaction — or short-term burning or itching. Some of these plants can cause a severe reaction and blistering.

Gardeners might find giant hogweed, baby's breath, leadwort, stinging nettle, and ragweed growing in their own gardens. 
Some very pretty ornamental and food plants harbor a potential for pain.

Some popular flowers, plants and crops that can 
cause allergic reactions or injury when handled

Below is a national map provided by the USDA of commonly-found 
and invasive plants and weeds that cause irritation specific to region

There are many others that you might be allergic or sensitive to.  For instance, pine sap gives me 
itchy hives  and swelling, but it's not considered to be something very common..  Following a jaunt 
to pick out my live Christmas Tree, I had an itchy and painful rash that lingered for hours, even 
after washing it off. I had to decorate while wearing gloves when reaching into the branches. 
The leaves and branches of the tomato plant drive me mad with itching, while I'm picking or pruning.

Injury to the skin is common from exposure to thorns, cactus spines, and spiny or sharp leaves, a popular culprit is stinging nettles. Punctures from rose thorns are well known. There are also thorns on the ornamental shrub barberry, and on some fruit trees. 

The tips of holly leaves are sharp enough to puncture the skin.
Spines from cacti are strong enough to do the same. Even small, nearly invisible "hairs" on cacti can be strong enough to puncture skin. I got rid of most of my outdoor cacti for this reason. Two layers of gloves didn't prevent the hairs from attaching to the skin.

Fibers on tulip and daffodil bulbs can cause injury, as can nearly invisible hairs on dogwood leaves. 
Sometimes, the puncture itself is the only injury. In other cases, histamine is released; there is a puncture wound, plus local itching. Any break in the skin can lead to infection.

English ivy (Hedera helix and related species) can cause an allergic skin reaction. Allergic reactions have been reported in gardeners after trimming English ivy and in children who played with English ivy or climbed trees covered with it. Itching, rashes, and weepy blisters can occur.

Some plants can lead to injury if sap or juice gets onto skin, and then that skin is exposed to sunlight. A red rash and possible blisters. As the skin heals, the affected areas may become much darker than usual; these darkened areas may take weeks or months to fade. 

Preventing these itchy and blistery skin reactions

• When gardening or doing yard work, cover as much skin as you can. 
• Wearing gardening gloves can prevent many plant materials from piercing your skin. Long pants and sleeves can prevent the rashes that occur when pieces of grass, weeds, poison ivy, and other plant materials are thrown back forcefully onto skin when weed-whacking.
• Avoid touching your face and eyes when working with outdoor plants.

Chemical irritation, allergic reactions, and light-sensitivity are all 
possible effects of exposure to certain plants – not just poison ivy

Poison ivy -  The most popular aggressive and unpopular guest wherever it can hide. It grows along roadsides, on fences, in backyards. Poison ivy leaves grow in clusters of three on vines that can grow up into trees or trail along the ground. Every part of the plant contains the compound urushiol, which causes poison ivy’s rash — the vine, the roots, the leaves, the flowers, and the berries.

Poison oak is not related to oak trees, although its mature leaves somewhat resemble those of an English oak. Like poison ivy, poison oak is found throughout the United States, and it grows in forests as well as in dry spots, like sandy fields. Poison oak has deep green leaves that grow in clusters of three on a firm stem. Its yellow flowers are often described as hairy, and its berries, fuzzy (unlike poison ivy’s smooth berries). 
Like poison ivy, every part of a poison oak plant contains urushiol in all seasons, meaning that any part of the plant can cause an itchy rash and blisters if you come into contact with it.

Poison Ivy Prevention
Follow these suggestions when handling all irritating plants and weeds

Note about burning poison ivy and other plants that cause irritation  - DON'T DO IT!!!  
The inhaled smoke carries the airborne toxins and histamines into your lungs, and itching or painful blisters can form. 
This is serious!

Plastic bags
Use plastic or heavy shopping bags to pull plants from the soil, replacing the bags with the pulling of each plant. Plastic bags can also be used to cover arms for additional protection during the removal process.

Get to the root
Any lingering shoots or seedlings can be killed with white vinegar.