In Shakespeare's Hamlet, two of Hamlet's childhood friends, Rosencrantz and Guildenstern, "being of so young days brought up with him," are asked by Hamlet's uncle, King Claudius, to find out why Hamlet is moping around the castle all the time and to "glean" what might be troubling him other than the death of his father.

Queen Gertrude tells Rosencrantz and Guildenstern that Hamlet often talks about them—which probably isn't true—and that if they can find out what Claudius wants to know about Hamlet, they "shall receive such thanks / As fits a king's remembrance." In other words, they can expect a handsome reward for their efforts.

From that point forward, Rosencrantz and Guildenstern are absolutely loyal and true only to themselves.

When Rosencrantz and Guildenstern meet Hamlet later in the same scene, Hamlet isn't fooled for a minute about their reason for being at Elsinore. Rosencrantz and Guildenstern do some serious tap-dancing around Hamlet's question, "Were you sent for?" Then they confer about the best way to answer the question, and they decide to look out for themselves. They immediately give away Claudius's plan.

GUILDENSTERN. My lord, we were sent for.

If they ever had any loyalty to Claudius, it's now gone.

The Players arrive, and Rosencrantz and Guildenstern stay around to see if there's anything that Hamlet says or does that they can report to Claudius.

When Rosencrantz and Guildenstern next meet with Claudius and Gertrude, in act 3, scene 1, they have almost nothing to report to them, so they lie.

ROSENCRANTZ. He does confess he feels himself distracted,
But from what cause he will by no means speak.. ...

GERTRUDE. Did he receive you well?

ROSENCRANTZ. Most like a gentleman...
of our demands, most free in his reply.

The best they can do is tell Claudius that Hamlet was happy to see the Players (which he was) and that Hamlet told them to invite Claudius and Gertrude to the play that evening (which he didn't).

Claudius decides to send Hamlet to England, and to make sure Hamlet gets on the ship and makes it to England, he tells Rosencrantz and Guildenstern that they're going to England with him. Rosencrantz and Guildenstern readily agree, if for no other reason than to get away from Claudius so he stops asking them about Hamlet.

In the meantime, while Rosencrantz and Guildenstern are packing for England, Hamlet kills Polonius. It's an accident, but this is good news for Rosencrantz and Guildenstern. Claudius's focus immediately shifts from "What can Rosencrantz and Guildenstern find out about Hamlet?" to "Where is Polonius's body?"

Unfortunately, Rosencrantz and Guildenstern can't get an answer from Hamlet to that question, either. Instead, they take Hamlet to Claudius, and Claudius finds out from Hamlet where Polonius's body is.

The plans for Hamlet's trip to England are still on, and Rosencrantz and Guildenstern are still going on the trip. They can finally get away from Claudius, and they can breathe a sigh of relief that they no longer have to answer to him for Hamlet's "madness."

Everything is going well for Rosencrantz and Guildenstern until Hamlet finds Claudius's letter to the king of England in their luggage and changes Claudius's request to the king. The pirates attack their ship, Hamlet is captured by the pirates, and Rosencrantz and Guildenstern have to continue on to England empty-handed.

Actually, they're not quite empty-handed. They still have the letter from Claudius to the king of England, which Hamlet changed to read as follows:

That on the view and knowing of these contents,
Without debatement further, more or less,
He should the bearers put to sudden death...

Hamlet has no remorse for sending Rosencrantz and Guildenstern to their deaths.

HAMLET. Why, man, they did make love to this employment!
They are not near my conscience; their defeat
Does by their own insinuation grow.

Hamlet says that they knew what they were getting into when they agreed to spy on him for Claudius and that they should have known better than to come between Claudius and him.

HAMLET. 'tis dangerous when the baser nature comes
Between the pass and fell incensed points
Of mighty opposites.

(Lesson learned, although a little late to do them much good.)

As Guildenstern says very near the end of Tom Stoppard's play Rosencrantz and Guildenstern Are Dead:

[T]here must have been a moment, at the beginning, where we could have said no. But somehow we missed it.

Though he can't remember their names correctly, Claudius summons Rosencrantz and Guildenstern to Elsinore so that, under the guise of friendship, they can investigate Hamlet's madness:

The need we have to use you did provoke
Our hasty sending. Something have you heard
Of Hamlet's transformation—so call it,
Sith nor the exterior nor the inward man
Resembles that it was.

They're loyal to Claudius because they obey him to the letter, interrogating Hamlet and reporting back to Claudius about him, though - by not being as bright as Hamlet - they do get caught out by Hamlet in the first scene they have with him. They try to play him, as he says after the play scene, like he is a pipe. But they are, of course, being loyal to their king.

There's an early sign of their loyalty when they rather toadily praise the king for asking them, rather than commanding them, to talk to Hamlet:

ROSENCRANTZ:
Both your Majesties
Might, by the sovereign power you have of us,
Put your dread pleasures more into command
Than to entreaty.

GUILDENSTERN:
                     But we both obey,
And here give up ourselves, in the full bent,
To lay our service freely at your feet,
To be commanded.

Loyal servants of the crown, indeed.