The Puppet Masters, by Robert A. Heinlein, 1951, New American Library
I've read quite a lot of Heinlein's early work but this is one I've missed. Until now. I really enjoyed it. But then I like all of Heinlein's early work, especially those considered to be his juveniles. This one isn't quite a juvenile but it still has the same flavor of adventure and excitement.
Most of you know that this is an alien invasion story, of course. A ship lands containing what come to be called "slugs," which attach themselves to the backs of people , through the spinal cord, and then take control over them. At first no one knows who is controlled and who isn't. But the human race soon comes up with countermeasures, such as having everyone strip to the waist. The war is on but there are many more twists and turns before the end, which I won't give away.
One thing a little different about this tale is that it takes place at an undefined future time after some great earthly war and after humans have begun to settle on both Mars and Venus. They have blasters and flying cars as well as space ships.
In 1994, there was a movie made from this book starring Donald Sutherland, but as I remember it was set in the modern day, without the futuristic elements. They don't necessarily have to be there to make the story a good one.
The slugs essentially appear to be single cells that function almost like a composite brain and I'm pretty sure this was a big influence on the Star Trek original series episode called "Operation Annihilate!" That first season episode featured single 'brain cell' looking parasites that rode the backs of people that they had taken over. The similarity is too close to imagine that it was accidental. The episode aired in 1967.