References to 'qots' are translated as ‘thorn’ or ‘thornbush’ in the NIV.

There are a couple of plants which might be the qots. They include:
1. Ononis spinosa - The spiny rest-harrow (if a thorn)
2. A member of the Carduus or Cirsium genus, although these are a thistle rather than a thorn. 

Ononis spinosa

Ononis spinosa - spiny rest-harrow. PICTURE: Stemonitis at English Wikipedia (licensed under CC BY-SA 3.0)

The spiny rest-harrow (Ononis spinosa) is a perennial growing plant which grows to about 60 centimetres in height. It has pink flowers from May to August and has of course thorns. It is found in a wide variety of habitats throughout Israel.

The Ononis spinosa is a particularly annoying weed in the barley fields. It is an upright weed which has sharply pointed spines along its 25 centimetre stems. 

Part of the curse on all man, for his sin, was that the ground would produce qots: "It will produce qots [thorns] and dardar [thistles] for you, and you will eat the plants of the field" - Genesis 3:18; "If a fire breaks out and spreads into qots [thornbushes] so that it burns shocks of grain or standing grain or the whole field, the one who started the fire must make restitution" - Exodus 22:

Meanwhile, Judges records that the elders of Succoth had taunted Gideon thinking that he could not defeat his enemies. After they were defeated Gideon returned to Succoth and "He took the elders of the town and taught the men of Succoth a lesson by punishing them with desert qots [thorns] and briers." (Judges 8:13-16)

The last words of David liken evil men to qots: 
Is not my house right with God?
Has he not made with me an everlasting covenant,
arranged and secured in every part?
Will he not bring to fruition my salvation
and grant me my every desire?
But evil men are all to be cast aside like qots [thorns],
which are not gathered with the hand.
Whoever touches qots [thorns] - II Samuel 23:5-7

Psalm 118:8-14 says:
It is better to take refuge in the Lord
than to trust in man.
It is better to take refuge in the Lord
than to trust in princes.
All the nations surrounded me,
but in the name of the Lord I cut them off.
They surrounded me on every side,
but in the name of the Lord I cut them off.
They swarmed around me like bees,
but they died out as quickly as burning qots [thorns];
in the name of the Lord I cut them off.
I was pushed back and about to fall,
but the Lord helped me.
The Lord is my strength and my song;
He has become my salvation.

Qots are also mentioned in Isaiah 32:11-14:
Tremble, you complacent women;
shudder, you daughters who feel secure!
Strip off your clothes,
put sackcloth around your waists.
Beat your breasts for the pleasant fields,
for the fruitful vines
and for the land of my people,
a land overgrown with qots [thorns] and briers -
yes, mourn for all houses of merriment
and for this city of revelry.
The fortress will be abandoned,
the noisy city deserted;
citadel and watchtower will become a wasteland forever,
the delight of donkeys, a pasture for flocks...

And in Isaiah 33:12"
“Now will I arise,” says the Lord.
“Now will I be exalted;
now will I be lifted up.
You conceive chaff,
you give birth to straw;
your breath is
a fire that consumes you.
The peoples will be burned as if to lime;
like cut qots [thornbushes] they will be set ablaze.”

Hosea 10:7-8 prophesied the destruction of Samaria the capital of the Northern Kingdom of Israel and predicts that the city will one day be the place of qots:
Samaria and its king will float away
like a twig on the surface of the waters.
The high places of wickedness will be destroyed—
it is the sin of Israel.
Qots [thorns] and thistles will grow up
and cover their altars.
Then they will say to the mountains, “Cover us!”
and to the hills, “Fall on us!”

There are two mentions of qots in Jeremiah. In 4:3-4 it it says:
This is what the Lord says to the men of Judah and to Jerusalem:
“Break up your unplowed ground
and do not sow among qots [thorns].
Circumcise yourselves to the Lord,
circumcise your hearts,
you men of Judah and people of Jerusalem,
or my wrath will break out and burn like fire
because of the evil you have done -
burn with no one to quench it. 

While in Jeremiah 12:12-13 it says:
Over all the barren heights in the desert
destroyers will swarm,
for the sword of the Lord will devour
from one end of the land to the other;
no one will be safe.
They will sow wheat but reap qots [thorns];
they will wear themselves out but gain nothing.
So bear the shame of your harvest
because of the Lord’s fierce anger.

Ezekiel describes Israel’s enemies as being like sharp 'qots', but he announces to them God’s promise that they will one day no longer have "malicious neighbours": "No longer will the people of Israel have malicious neighbours who are painful briers and sharp qots [thorns]. Then they will know that I am the Sovereign Lord." - Ezekiel 28: 20-24

This is an edited excerpt from Alvin Johnson's iBook 'Biblical Flora', 2017. The book is available for free download on iTunes. A teacher's edition is also available for purchase.