The critter in the video is absolutely not a planaria. They can only glide, they cannot swim like that at all. It appears to be one of what are often called detritus worms. If you see worms similar to that one that are a distinct pink colour and swim like that, they are Dero worms. Small annelids, the only member of their family that is water dwelling. They make first class live fish food. Many farms and hobbyists culture them as food, they're terrific. They are so slim, even quite tiny fish can eat them.
You can get a pile of things hitchhiking along with plants or even the water they come in, as jcolon said. Copepods, various worms, planaria, even ostracods [ seed shrimp], or scuds; scud is a derogatory name for an amphipod or gammaru. They are actually quite good algae eaters, but if they are hungry, they will eat live plants as well. They make great fish food for bottom feeders, being one of the numerous small crustacean species, and if you don't overfeed, and have fish, their numbers stay under control quite easily. I actually culture them as live food, as well as ostracods, copepods and other things.
Scuds are also thought to prey on newborn shrimp.. and they are much better equipped to do that than planaria are. So if you have scuds and some baby shrimp, you might want to try to control the scuds more. Kuhli loaches and cories like to hunt and eat them, that's what I feed them to.
To try to cut down on the number of mystery critters, it is a good idea to rinse, soak and perhaps dip any new plants before they go into your tank. I leave mine in a bucket with a light and an airstone for a day or two at least. This won't get everything off but scuds tend to head for the bottom, and many of the small pest snails tend to end up the bucket sides. So that allows me to remove most of them.
If I have any worry about a given plant, or the bucket shows that it has a lot of things with it, I've tried dipping. First time I tried to dip anything, I melted a bunch of nice Wendelov ferns, using too much Excel. But you can use Hydrogen peroxide, Postassium Permanganate, Excel or household bleach as a dip, mixed to the right strength. Has the additional advantage that it kills any algae the plant has on it, along with most critters. I think Rivercats, on this forum, has great experience dipping plants, more than I do for sure.
Once you get some fish, you'll find many of these critters soon vanish, simply because they do make good fish food. Meantime, they are harmless. Even planaria are not the horrors that many say they are, unless they are the gigantic Asian species. If you have those you won't have trouble with ID.. they get to more than inch long, quarter inch wide and are not only unsightly, they're big and fast enough to be a danger to some of our fishy pets. Our native North Amercian planaria species are so much smaller. About 3/8" long, flat, and they do have a slightly triangular shape head end, with two 'eye' spots.. might need a magnifying glass to see these features. They feed mainly on biofilms and anything they find as they glide over them but can't really hurt much of anything, with the possible exception of newborn shrimp.
I am not sure about the shrimp, I've yet to see this happen. I've seen claims they can kill baby shrimp but they have no teeth, jaws or claws. They only a stomach on the underside, and eat by secreting juices onto the item beneath them and dissolving it, to suck up. Any shrimp that's healthy is just going to walk away, I'd think. If it's sick, hurt or dead, that's another story. Fish and shrimp both eat other dead fish and shrimp, so do snails. Better that they do, saves the deceased critter from spoiling your water.
The one beastie most of really don't want to see is a Hydra. Most species we see in tanks can't hurt much of anything, but the exception is that they can kill fry and baby shrimp. They work like a jellyfish, having some number of tentacles on the 'head' end equipped with stinging nematocysts that are fired into any animal that comes close enough. The tentacles draw inward as they fire the 'poison darts', bringing the critter they killed with them if it's small enough. They have a very tiny mouth being at the base of the tentacles, so they can't always eat what they kill. They can't hunt, only sit still and wait for prey to come close enough to trigger the response to sting.
They can move, by closing the tentacles and sliding along. At such times they look like slightly thicker nematodes. But they will find a spot to stop, anchor their base and open the tentacles, then you see what they are. Never try to kill one, they are immortal, even a cell or two can regenerate into new animal. So if you crush or damage one, you get many more in a short time. They can come on plants on in water too.
Siphon them out, get Spixi snails to eat them, or some fish, such as some of the gouramis, will eat them. Sometimes you might be able to borrow a spixi snail or gourami to take care of them. Again, they are not true horrors, they make good food for some fish, but if you have fry or breeding shrimp, you don't want them around.
