If a user download commercial software through the official, corresponding website, but use a product key which you did not legitimately purchase (e.g. websites that offer a list of product keys for free), does that harm anything other than the company who made the piece of software?
I was wondering if the person who generated those product keys can see which user(s) have used that key and are able to harm them in any way.
No.
Only the manufacturer of the software can know what key you have used and only if the software "calls home" for (re-)activation. Using a non-original key (for example, one provided by a key generator) will not give anyone back-door access to your computer/program.
In short: yes. Any software can harm you.
Legally: If the authors of the software find you are using illicit copies of their software, they are at liberty to file a civil copyright infringement claim against you. Software commonly "phones home", even in the form of checking for new updates. They may not go after you if you're a poor individual, but they love taking businesses to court, even if it bankrupts a small business.
Technically: Some authors have even put in attack code that runs if you use their software with a well-known pirated product key. This might be funny (for example, the game Crysis gives pirates a gun that shoots chickens instead of bullets) or it might be serious, like deleting all your personal files.
Morally: The software authors trust you to buy their software legally; you abuse that trust. You trust them to leave your computer unharmed when they find you using an illicit key. What if they abuse that trust? If they delete your entire hard drive when their software recognises an illicit key (regardless of phoning home -- software can have an embedded list of known pirated keys), what are you going to do about it?
Ultimately, your piracy might drive the authors to other means of making money, such as selling your personal information, which harms everybody, including licit users.
Personally, I would recommend you find free software that allows you to achieve the same aim, instead of using cracked proprietary software. Instead of cracked Windows, use Ubuntu. Instead of cracked Photoshop, use GIMP. Instead of cracked Word, use LibreOffice. Instead of cracked Maya, use Blender.
I'm not an expert in the matter, but if you have a legitimate copy of the software in question and not a "cracked" copy then the main concern for you would be that the company that created the software would know that the key you used is not yours (you're the 300th person to use it). From there they could either prevent the software from working or attempt to take legal action. I've never heard of someone that I know of having legal action taken against them. If you're using a product key as a kind of "trial" mode then you're probably just fine; although, I obviously don't suggest outright pirating the software.
If you're using a cracked copy that includes a product key or is "pre-activated" you are at the mercy of whoever cracked it and I wouldn't trust that at all.
One thing that has not been mentioned in the other answers: although using an illicit key might or might not be harmless, it usually correlates with malware infections - the key-generator, the key distribution website etc. are likely to contain trojans or other malware targetted at the less-savvy users.
A lot of software "calls home" nowadays. So using a cracked key, you may be broadcasting to the software editor that you pirated the product. Whether they sue you or not is their prerogative, but that sure looks like harmful to me.
Your computer would probably be fine, but I wouldn't trust the files it manages. An infamous company, "Yoyogames", decided to have a little fun with people pirating their software. They overwrote the user's images with skulls and crossbones.
The problem, of course, was a false positive destroying legitimate users' work.
This obviously depends on what type of software you are talking about, and what position the persons who cracked it are in.
If the system connects to some central server on a regular basis to verify that the product is legitimate, and that it is unlocked with a legitimate key, then I suppose there is a chance that someone could get compile a list of users using the same key. That again, requires this "someone" to have access to the server the software connects to for verification.
Whether this "someone" is in general likely also to be the person who generated the illegitimate key would be speculation. If anything, I would be more worried about the company behind the product coming after you for using an illegitimate key (though I suppose they would be more likely to just disable it, rendering it useless).
In essence, it boils down to this:
If you are just entering an activation-code into a legitimate piece of software, there is little chance of anything bad happening (unless the software communicates with a central server which just happens to have been hacked).
If on the other hand you use a piece of software that has been changed somehow (e.g., downloaded from somewhere other than the vendor's official site, or cracked using some other automated tool), then you can't really know whether or not your software can be trusted.
In some circumstances, yes. The software silently downloads an update and the update sees the key is blacklisted--and quits working at an inopportune time. (Say, in front of clients or prospective clients.)
I'm surprised that nobody has mentioned the invincible Red Scorpion in Serious Sam 3 as an example. Pirated versions of the game had this unkillable enemy that would appear and attack the player.
A product key that is found not to belong to you, when it "calls home" to activate, could trigger some unwanted feature in the software.
Maybe
If the key is used to encrypt sensitive data, and that key is reused in multiple locations, then your privacy is at risk.
Consider a serial number for 1Password that encrypts the local database. If that serial number gets out on the net, it's possible that that key can be used to decrypt the corresponding secrets. (1Password doesn't work this way, but it's an analogy )
Not directly, but I can see 2 indirect ways:
A key, by itself, cannot compromise your computer in any way, unless the software is explicitly programmed to act maliciously in response to a cracked key (it's still a question how it will tell which keys are cracked...). The key is just a password for you to prove that you have the right to run the software (ie. that you obtained a license to that program by buying it).
But this is a bit of a moot point because no one just uses a cracked key for no reason - they use it because their software is also cracked (so #2) and even if you have legally obtained software, just putting in a cracked key is not necessarily safe (because of #1).
In the olden days it used to be that programs would simply run a mathematical operation on the key and decide whether they accept it or not (and even earlier, there would literally be a few questions with a secret answer). The exact algorithm would be secret and hard to guess, so you would basically only be able to run the software if the developer generates a correct key for you. Crackers would reverse engineer the algorithm and generate their own keys - it's hard to see how a software could distinguish between keys generated by copyright infringers and keys generated by the developer (in fact, its ability to distinguish this was the algorithm in the first place, and that has already been defeated at this point). Granted, often the crackers then distribute the key generator with a virus in it, so there's that.
After internet became ubiquitous, companies have moved on to just maintaining a list of keys they received payment for, and making software phone home to check. Now "cracked keys" come from someone who works at a company with a volume licensing key, who then leak that key. If the developer catches on, they may revoke that key to render it useless. Since the key was intended to be legitimate (and initially was), it's hard to see how it would harm your computer. But, like I said, if the software phones home, you'd be making yourself conspicuous.
AAAA-1234-BBBB-5678and enter that into the license page. It is quite another to download some software that prints out the product key.AA...online, or downloading some a key generator. The two options have very different risks on a given machine. I bring this up because there is a fair bit in the comments on the answers that the OP may not be aware of. It would be helpful if Ben would clarify the means of obtaining the keys.