Some Star Wars Droids are definitively sentient beings, but it appears that they are not treated as such.
The Legal Status section of the Droid article of Wookieepedia (which have no references) said they are typically treated as property, but does the status change along with the various governments? Is there any known canon occurrence in the expanded universe where consequences of the destruction of a droid have been explored?
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.
Edit: 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).
You will definitely be interested in the, now Legends, telling of IG-88's backstory, related and summarized in his Wookieepedia entry and also via the Inside The Force podcast, if you can't get your hands on the source material.
In fact, there was a number of attempts at droid revolts throughout the Legends history of Star Wars.
Ultimately, however, droids are considered inferior beings and not afforded the rights and standing of biologicals. The resolution over the destruction of another's droid would likely be resolved similar to the destruction of an individual's property. The sentience of the droid would not be considered, however, the emotional stakes or damages to the owner losing the droid could be accounted for within the damages.
For example, in most jurisdictions, the destruction of another's livestock is merely treated like property, however, the destruction of another's pet doesn't arise to penalties equivalent to killing a member of that person's family- even if that is how the pet is perceived by the owner- however the penalties will be more significant than the destruction of livestock to account for the owner's feelings. In both cases, an additional penalty may be assessed based on the cruelty or suffering the animal may have endured, not necessarily because of the recognition of the animal's life, but more to penalize and stigmatize the behavior of the perpetrator. Where behavior was the intentional infliction of emotional distress upon the owner, additional penalties may be assessed.
However, this sentimental measure applies to inanimate objects as well. Destruction of someone's family album will garner a more serious penalty than simply paying the cost to replace the physical album and photo medium.
Therefore, largely droids would find themselves somewhere between livestock, slave, and pet in terms of possible recoverable damages against others who wrongfully damage or destroy another's property.
