The discovery of five planets around 55 Cancri, a sun-like star with one of the planets in the habitable zone brings the question of the Fermi Paradox even more into the forefront.
Solutions to Fermi's paradox often come down to either 1) life is difficult to start and evolve (either hard for the process or hard to find the right conditions) or 2) advanced civilizations destroy themselves on short timescales. In other words, this is an important problem to solve in the hope that it is 1 and not 2.
1. They Are Here
They Were Here and They Left Evidence
UFO's, Ancient Astronauts, Alien Artifacts: all fall under the heading of proposals that aliens are here now (and they call themselves Republicans) or have been here in the recent past. Problem: evidence for aliens is non-existent.
They Are Us
Humans are the descendants of ancient alien civilizations. Problem: where are the original aliens? Where are all the other alien civilizations
Zoo/Interdict Scenario
The aliens are here, and they are keeping us in a well designed zoo (cut off from all contact) or there is an interdiction treaty to prevent contact with young races (us). Problem: scenario lacks the ability to be tested. Takes only one ET to break embargo.
2. They Exist But Have Not Yet Communicated
They Have Not Had Time To Reach Us
Speed of light slows communication levels, relativity makes space travel long. ET's message may not have reached us yet. Problem: Galaxy has been around for billions of years, even if one ET civilization formed a few million years before us, the Galaxy would be filled with Bracewell-von Neumann probes.
They Are Signaling, But We Do Not Know How To Listen
EM radiation, gravity waves, exotic particles are all examples of methods to signal. Problem: they may use methods we have not learned yet, but if there are many civilizations someone would use EM methods.
Berserkers
The Galaxy is filled with killer robots looking for signals. ET is keeping low. Problem: where are the berserkers coming after us?
They Have No Desire To Communicate
ET has no interest in conversing with lesser beings. Problem: with millions of possible civilizations, someone would have some curiosity.
They Develop Different Mathematics
Mathematics is the universal language. But humankind may have a unique system of mathematics that ET cannot understand. Problem: then where are their incomprehensible signals?
Catastrophes
Civilizations only have a limited lifetime, They are all dead.
Overpopulation
Nanobots -> Gray Goo Problem
Dangerous Particle Physics
3. They Do Not Exist
We are the First, Life is New to the Galaxy
Life is new to the Galaxy, evolution takes time, we are the first civilization. Problem: Sun is average star, if other stars formed a million years ahead of us, then They would be a million years ahead of us in technology.
Planets With the Right Conditions are Rare
Planetary systems are rare
Habitable zones, proper distance from star for liquid water, are narrow
Galaxy is a dangerous place (gamma-ray bursters, asteroid impacts, etc)
Earth/Moon system is unique (large tides needed for molecular evolution)
Life Is Rare
Life's Genesis is rare
Intelligence/Tool-Making is rare
Language is unique to humans
Technology/Science is not inevitable
http://zebu.uoregon.edu/~js/cosmo/lectures/lec28.html