Wired connections have some properties that wireless connections don't:
Robustness: a wireless connection can be subject to various forms of interference (think to microwave ovens) and obstacles, that can affect the quality of the received signal.
Latency: wireless connections make a large use of acknowledge signals and error checking codes, due to their lower reliability. This means that you need to wait more for valid data.
Parallelization: while you can run 10 cables to transfer 10x signals, with wireless links it's harder because you will have interference and a limited amount of channels. This applies also when you have many networks in the same place.
Security: with a wire you (almost) always know where you're sending the signal, and getting into a wired network requires at least to get access to the cable. With wireless connection the thing is much harder, because signals are broadcast in the air. Encryption systems are evolving, but with GPGPUs and parallelized computing it's becoming much quicker to make brute force attacks.
Range: you know the range of a wired connection if you have the specification and a long enough cable; it's harder with wireless networks because they are subject to reflection and all the obstacles on the path, and estimating the range is mostly by trial and error.
Safety: this is a minor point, but there is research about the effects of RF on the human body
As a side note, there are some applications (think to smartphones) which are only possible with wireless connection. So the odds are that both communication media will survive also in the long term.