The book 'The Courtship of Princess Leia' mentions (in passing) an activist group for droid rights (when Threepio asks to address the Senate, who for some reason have a say in who Leia can marry).
Under the Empire, droids had no rights.
I haven't read anything after the Vong invasion, so I can't speak to that.
In general, consensus for thousands of years has had droids as property, with rare ones as independent operators (though their legal status is questionable).
There is a definite indication that the New Republic was more lax in this - Threepio WAS permitted to address the Senate, and state a contrary opinion, without any significant repercussions, but droids ARE generally property.
And it makes sense - droids are manufactured for tasks, engineered and designed with a purpose in mind, do not self-reproduce, are marketed and purchased, easily controllable by commercially available items (restraining bolts), and - with regular maintenance and routine wipes - completely lacking in distinct individual personality.
Droids like R2 and C3-P0 are unusual (owing to their history, if nothing else). Most droids do not even approach their level of personality or individuality.
As to whether this is RIGHT (ethically), I can't speak. Certainly we've seen that droids have the potential to be more than property, but there has never been a general emancipation of them.
It's even likely that, were there to be a general granting of rights to droids, they would cease being created (or new droids would lack the capabilities that are at the core of what gave droids rights) - it wouldn't make fiscal sense for a company to produce end products which they would be unable to sell.
To more correctly answer your secondary questions:
It's never explicitly stated what happens (legally speaking) to someone who destroys a droid. They have no intrinsic rights, so it would be treated (under every government I'm familiar with) as destruction of property. If you legally owned the droid, nothing would happen except that you wouldn't have a droid (unless the droid had some special circumstance, such as having evidence in another legal matter, in which case it's destruction could be obstruction of justice or similar). If it was another's droid, it could legally be considered destruction of their property, and punished as such.
If the droid was state property (battle droid, court recorder, maintenance droid, etc) it would be destruction of government property.
If the droid had no owner, like with IG-88 (the independent assassin droid), there would likely be no legal repercussions (well, maybe 'littering' if you left it lying there, or 'disturbing the peace' if you caused a big ruckus in destroying it).