the thing about psi powers is that it may not be psi powers at all....it just might look like psi powers to the untrained eye (That's the whole premise of Psyche
For instance, in the TNG ep "Cause and Effect," Data gets the android equivalent of a premonition. However, watching the episode we get a TECH reason for the message.
Babylon 5 is another example of this. From the very first episode we see that the Minbari believe in prophesy. Their prophosies had an uncanny way of comming true. Its only later do we discover they are the result of a pre-destination paradox.
The new BSG
has by no means conclusively included supernatural elements. Its intentionally left ambiguous. So far most of the things that have happened have been given rational explanations. The same was true on Lost
until very late in the game.
As for shows without supernatural elements....
Total Recall 2070
Space Above and Beyond
Sliders (Sliders is a unique case since the very nature of the show opens the potential for "different" physical laws in other universes.....its a stretch though)
Century City (one cannot help but notice that most of these did not get more than one season...if that)
Jericho (is this sci-fi)
Mann & Machine
Planet of the Apes
Primeval (conditionally...we do not know the origins of the rifts)
Viper (once you accept Knight Rider you get all of its copy cats)