Horatio:
In a play about madness, Horatio seems to be the voice of reason. Our first indication of this is his scepticism about the appearance of old Hamlet’s ghost. Horatio eventually accepts the ghost, although only, as he says "[because of] the sensible and true avouch of mine own eyes"(1.1.57), suggesting his need for tactile evidence. Horatio’s character is noticeably 2-dimensional in that he seems (until the final scene) untouched by the tragic events, and is the only major character who isn't engulfed by the madness of the play.
Horatio can be seen as a sort of sensible shadow, or mirror, by which Hamlet’s words and actions can be measured. Most of the time, Horatio’s lines are affirmations of Hamlet’s own sentiments ("Ay, my lord", etc.), like in the grave-digging scene (5.1) where Horatio serves as a sounding board for Hamlet’s thoughts about mortality. Upon Hamlet’s return from England, however, Horatio’s line, "what a king is this!"(5.2.63), appears to be a definite negative judgement on Hamlet’s murder of Guildenstern and Rozencrantz. In this, Horatio demonstrates that he is not simply a projection of Hamlet's mind, but also an ideal that Hamlet may not necessarily live up to.
In act 3, scene 2, Hamlet comments on the nature of his relationship with Horatio (54-85), and proclaims him to be his closest and most trusted friend. Hamlet comments that Horatio is "not passion’s slave"(72), and that he "wear[s] him in [his] heart’s core"(73). This scene works very well with the Horatio-as-a-manifestation-of-reason model, as it shows the parallel between Hamlet’s relationship with Horatio and his relationship with reason. For instance, while Hamlet claims to hold Horatio "in [his] heart of heart"(73), he spends very little time with Horatio, and never listens to (or even asks for) his advice. Likewise, Hamlet spends much of the play trying to temper his passion through contemplation, although his actions, far from rational, are dominated by madness. Thus, it could be said that while Hamlet places a great deal of value on Horatio and reason, the voices of both eventually fall on dead ears.