Music, as an art, is in the ear of the listener. As a musician, I can say there are definitely times when a song sounds "better" in one key than another.
The primary reason this is so is when the key fits the "natural" range of a singer or instrument. A song may sound perfect when sung by a female alto, but as those notes sung verbatim would be at the top of a male vocalist's range or, if transposed, the very bottom, it would very likely sound "off" (regardless of subject matter) if sung by a male in the original key, because you will hear the strain in his voice, or the timbre changes as he moves from his chest voice into either his head voice or to pedal tones. Transposed down a fifth into a new key, the song would sound much better when sung by a male singer. The same applies in reverse.
In other cases, such as stringed instruments like guitars, there is a mixture of convenience and of chord voicing. Guitars, because of the tuning of their open strings, have a few "natural" keys, like G and D, in which the most common chords heard in a song of that key (I,ii,iii,IV,V,vi) are easy to play. Also, because of the tuning intervals between strings and the subsequent natural spacing of notes in guitar chords, the playing of a song in a different key often necessitates the use of chord fingerings which produce alternate voicings; a different note in the chord will be on bottom and on top, and different notes will be next to each other. This can definitely make a song sound better or worse depending on key.
Even in cases of instruments like pianos, where theoretically the instrument has the same timbre across the entire instrument and the same chord voicing can be played just as easily in any key, there are changes in timbre as the pitch changes. This is due to differences in construction across the same instrument (a piano for example goes from one to two and three wound strings, and then to three monofilament strings, for each key of the keyboard as you move from left to right) and due to simple physics (for instance, as notes increase in pitch, we hear less of the harmonic overtones produced as they pass beyond 40kHz, and conversely, as pitch decreases and heads toward the subsonic range, the frequency difference in notes and thus our ability to perceive said difference diminishes). This may lead to a song sounding better in a lower (or higher) key for reasons that may not be explainable at the time.