Basic Trope: Humans are the only intelligent form of life.
Straight: In a Space Opera setting, humans have explored far into the galaxy and discovered no intelligent life.
Exaggerated: They can't even find single-celled organisms, despite sending probes to every habitable planet. Life itself only ever evolved on one planet, Earth.
Alien life has evolved to the level of animals at most, but is non-sapient.
There are some alleged UFO sightings every now and then, but otherwise no definite evidence of alien life.
Human space travel is in its infancy, and we haven't had time to find them yet.
The odds of contacting intelligent life forms are so low that, even if they are there, it might take a million years to find one.
There was a large, multi-species empire that was wiped out somehow.
Inverted: The universe is full of aliens, but humans don't exist.
Subverted: Humans finally discover an alien civilization, and quickly make First Contact.
Double Subverted: The 'alien civilization' was actually a long lost human colony.
Zig Zagged: The starship Lazarus searches 1000 earth-like planets for intelligent life. Some of them offer false leads, but all of them are uninhabited. That is until the last planet they look actually does support an alien species, but it is non-sapient. However they find out the intelligent aliens were posing as non-sapient to see how the humans would treat them. Then it turns out that they are actually highly evolved humans, and the starship's crew had experienced 50 million years worth of Time Dilation.
Repeated radio signals of "Hello, we come in peace." from a specific point in the sky turn out to be random noise. The cosmic background radiation just happened to make that pattern.
The aliens are obviously present and even attempt to communicate with the humans, but the humans are too stupid or attached to their preconceptions to recognize the aliens' presence.