It has been observed that of the stars we can see, a greater part of
them belong to binary systems, where two stars move around each other.
 It seems that our sun is a single star system, but is this indeed the
case?

Yes, otherwise we'd have two suns. There is the possibility that there
is some gigantic star, or it'd probably have to be a black hole, way
far away, with which the sun is in a binary system, but then we would
observe an irregular "wobble," as well as an irregular orbit, which we
don't. The sun, however, is orbiting the center of the galaxy, but
this is not counted as a binary system.

Some related ideas:

Nemesis: Does the Sun Have a 'Companion'?
http://www.space.com/scienceastronomy/solarsystem/nemesis_010320-1.html

Can planets evolve in a binary star system? If no, why? 
http://www.madsci.org/posts/archives/dec97/878075280.As.r.html

The experts seem to differ on both parts of your question.
 In my humble opinion, a class m star presently perhap ten lightyears
away, may have passed much closer several times in the past billion
years. That fits the definition of binary, but the class m star is
preturbed near it's maximum distance, so it may return only one more
time or zero more times, so we would no longer be a binary star in our
future even though we were for the past billion years.
 Some arrangements of some binary stars eject the plants, by
perturbing over the long term. IMHO, other arangements allow stable
planitary orbits for billions of years, even in systems with more than
two stars.   Neil