This really depends on what part of the world you are in.
There are leeches in Australia that live in wet undergrowth (fronds, plants, etc) next to trails.
When anything edible walks past they grab hold and start feeding.
You don't even notice them until they drop off and the bleeding starts (since they inject anti-coagulant and numbing agent).
I've experienced this myself, it was common when we went hiking in the rainforest to have multiple leeches on us by the time we finished the hike and you would have no idea they were there until you rolled up your trousers.
In my experience they don't drop down onto you though, they wait in bushes beside the trail and grab on as you walk past.
This is why you generally get them on your legs, and not anywhere else.
outdoors.stackexchange.com/users/3548/Tim B
Yes, leeches can live above ground, on trees, and drop on their prey.
I have seen this happen while hiking in Nepal.
The leeches of which @ShemSeger speaks of are water leeches, but leeches also include the haemadipsidae family, which are ground leeches.
They will do amazing things to reach you, including (but not limited to) dropping on you from above.
outdoors.stackexchange.com/users/483/Eyal
Leeches swim in still water, they don't live in trees, and they don't dwell on the ground.
They attach themselves to bare skin, you won't even notice them do it.
Last time I had a leech latch onto me
I didn't find it until that night when I went to bed and found it mostly dried up attached to my toe when I took my socks of to get into my sleeping bag.
(it was just a small one, somehow I didn't notice it when I put my socks on after getting out of the water).
I think what you're thinking about is perhaps not leeches, but ticks .
Ticks will climb up onto tall grass or shrubs and hang out with their long arms up in the air just waiting for something to walk by that they can grab onto.
They then crawl up your body and will either go under your shirt and attach to your back (the only place I've ever had them attach to me) or they'll climb right up to your neck or get into your hair and latch on to your scalp.
You might notice them crawling on you, but you usually find them after they're already attached.
To get them off all you have to do is get a good hold on their bodies, give them a gentle tug–just enough to raise your skin to where you can really feel it pulling on you–and then hold it there, they will eventually lose their grip and come off.
Don't try to rip them off, just hold on and and wait for them to let go,
if you rip them off you could rip their bodies from the head that's lodged inside you, which will likely get infected, and I don't know about you but the idea of having a severed head stuck under my skin kinda grosses me out.
Leech:
Tick:
outdoors.stackexchange.com/users/4148/ShemSeger
From my personal experience in the Western Ghats of India: I have found them in still water.
They dwell on the ground hunting for prey.
They can climb up trees barks and search for the heat signature of animals.
They are found only in regions with considerable wetness.
ADDITIONAL INFO:I do not think this is specific to any region of the world.
As long as they have a wet patch of land to dwell on, they'll be around.
They wont harm much.
They use two chemicals: An anticoagulant(hirudin.
Proven and well documented) to prevent blood from clogging and a local anaesthesia(not proven yet) to prevent you from feeling their bite (Some even suggest morphine).
So basically, they attach on to you, bite with the chemicals in place, and sit there opening their mouth while your blood drips into them :P.
They are more of a nuisance.
And yes, they are kinda squishy and feel weird to touch.
Number of leech bites I've had: At least a thousand till date :D
outdoors.stackexchange.com/users/2066/Ricketyship
Yes, it can happen.
I took a trip to the Amazon during and after the time when the river rises and turns the rain forest into a lake.
After the water reseeds, sea animals get stuck in pools in trees.
When you walk through the jungle they sense/feel your body heat and drop out of the trees on unsuspecting prey.
outdoors.stackexchange.com/users/15893/Kenneth Stevenson
Do leeches fall from trees onto unsuspecting hikers?    Or do they only dwell on the ground and attach to passing feet/boots?
Do leeches fall onto prey from trees?
outdoors.stackexchange.com
<leeches>
outdoors.stackexchange.com/questions/8160
outdoors.stackexchange.com/users/3335/WW.
Some say that leeches  can live above ground, on trees, and drop on their prey. This really depends on what part of the world you are in.  Others say that they swim in still water, they don't live in trees, and they don't dwell on the ground. There are conflicting views on the ground, but leeches can drop onto prey from trees.
Leeches do drop onto prey from trees. There are conflicting views on leeches staying on the ground.