I don't think we can really call him a slave - if he is a slave, he isn't a very good one, and the people around him seem to treat him as a fellow creature, albeit one who is inferior to themselves. They get annoyed with him on more than one occasion, but they also appear to have some degree of affection for him.
He does seem to make some decisions on his own, and he definitely disobeys orders on more than one occasion.
When Luke and Owen buy the two droids, Luke takes them into the maintenance room and starts working on them. R2-D2 plays part of Leia's message to Obi Wan, and Luke asks him to play the whole thing. By this time, 3PO is already referring to Luke as "master". R2 has 3PO tell Luke to remove his restraining bolt, and Luke does so. This allows R2 to refuse to play any of the message. Luke is mildly annoyed, and orders R2 to play the message again. 3PO lies to cover up for R2, making an excuse for him - "His behavior is erratic", or something along those lines. When Luke leaves the room, 3PO says "He's our master now - just you reconsider playing that message". This makes it pretty clear that 3PO has just defied his master's will.
In Return of the Jedi, when the group is captured by Ewoks, it becomes clear that the Ewoks think C-3PO is a god. Luke orders 3PO to exploit this to their advantage by pretending to be a god, and 3PO explicitly refuses to do so. Luke insists, and at length, 3PO relents. But it is important to note that, at least for a moment, 3PO refuses to obey a direct order from his ostensible "owner".
In a deleted scene from The Empire Strikes Back, C-3PO is fleeing the rebel base on Hoth with Han, Leia, and Chewbacca. He stops in front of a door, peels off a warning sign, and hurries after the others. Shortly afterwards, Stormtroopers find the door and open it. They are immediately attacked by Wampas. The scene was deleted because the Wampa effects didn't work properly, not because the content of the scene was a problem. This is an example of C-3PO making a decision on his own, with no instructions from anyone else. I would call this free will.
In the first movie, when the droids are left alone in the hangar control room aboard the Death Star, 3PO lies to a Stormtrooper in order to get away from the Imperial troops. We have no reason to believe that Luke told him to do so, and although this doesn't qualify as refusing to obey an order, it does imply a degree of autonomy, or free will. He made the decision on his own, with no instruction from anyone else.
Throughout the original trilogy, C-3PO constantly argues with the people who are technically his superiors - people whom he refers to as "master". He questions Han's decisions at every turn. He insults Chewbacca on a very frequent basis, most notably (and perhaps understandably) when Chewie puts his head on backwards. He often says things which are mildly insulting about humans, sometimes going so far as to call them rude to their faces.
He doesn't attempt to hide his disgust at Jabba and his minions, despite the fact that Luke has given the droids to Jabba, making the Hutt their new master.
When Lando attempts to save Han, after having betrayed the group, Chewbacca attacks Lando and Leia makes it clear that she supports Chewbacca's actions. 3PO takes it upon himself to vehemently oppose Chewbacca and Leia, almost screaming "What are you doing! Trust him!" When Chewie finally backs off, 3PO apologizes for him, saying "He's only a Wookiee". Whatever 3PO's status may be, it seems safe to assume that Chewbacca outranks him, but this fact does not prevent 3PO from constantly insulting him - if you said the same things to Chewbacca, he'd probably rip your arms off.
C-3PO is not the equal of Han, Leia, Luke, and Chewbacca - and in fact, he is probably less respected than R2-D2 - but they clearly don't see him as a slave or a mere object. Despite all their frustration with his griping and whining, they value him as an important member of the team, and they put up with his annoying behavior on most occasions. When the situation is dire, they might shut him down so they can concentrate on the task at hand, but this is just a more effective way of saying "Shut the hell up for a minute and let us think!"
When Chewbacca finds 3PO in pieces on Bespin, he fights with the weird little creatures who are about to destroy 3PO, and once he gathers all the pieces together, he appears to genuinely upset about 3PO's "injuries" and shows what might be considered sympathy for him. Leia has a similar reaction to seeing him in pieces. When Chewbacca is locked up in a holding cell, he immediately starts to reassemble the droid. This suggests a certain level of concern for 3PO's wellbeing.
It goes without saying that Luke loves R2-D2, so it isn't hard to believe that the group feels more or less the same way about his less endearing counterpart. Sure, he has his faults, but they wouldn't keep him around if they didn't care about him. The fact that they are willing to put up with his nonsense is indicative of a deeper feeling of affection for him. Why would anyone tolerate all the negative aspects of his personality unless they cared about him enough to overlook those flaws? He is certainly at the bottom of the totem pole, but at least he is on the totem pole.
If the others saw him as nothing more than an object, like a trash can or a computer, they would have no reason to accept his idiosyncrasies. They would simply get a newer, better droid who wasn't so annoying. They never do so because they like him and value his contributions to the mission. He is a member of the team, and not merely a possession.