There are many examples of monologues, or long speeches made by a single character in literature. Often these speeches are made to express their mental thoughts, but they are also sometimes a direct address to another character or even the audience. Here are a few examples of such presentations off the top of my head:
In the play Hamlet, the title character offers a long soliloquy (the act of speaking one's thoughts aloud when by oneself or regardless of any hearers, especially by a character in a play) that begins, "To be, or not to be--that is the question..." It is a well known passage that goes on to say:
Whether 'tis nobler in the mind to suffer
The slings and arrows of outrageous fortune
Or to take arms against a sea of troubles
And by opposing end them. To die, to sleep--
No more--and by a sleep to say we end
The heartache, and the thousand natural shocks
That flesh is heir to. 'Tis a consummation
Devoutly to be wished. To die, to sleep--
To sleep--perchance to dream: ay, there's the rub,
For in that sleep of death what dreams may come...
This is also a form of direct address because at points in the monologue Hamlet is addressing the inanimate object in his hands (a skull).
Direct Address (to a Character)
In one of my very favorite movies A League of their Own, the team manager directly addresses his female right-fielder after makes a stupid play and then starts to cry on the field:
Which team do you play for?...Well, I was just wondering, 'cause I couldn't figure out why you'd throw home when we've got a two-run lead! You let the tying run get on second and we lost the lead because of you. Now you start usin' your head! That's that lump that's three feet above your ass!...Are you crying?... Are you crying? ARE YOU CRYING? There's no crying! There's no crying in baseball!...Rogers Hornsby was my manager, and he called me a talking pile of pigs--t, and that was when my parents drove all the way down from Michigan to see me play the game! And did I cry?... No! No! And do you know why?... Because there's no crying in baseball! There's no crying in baseball, no crying!
Another example can be found in the movie A Scent of a Woman where, Lt. Col. Frank Slade's (played by Al Pacino) gives his famous 'Out of Order' speech at the end of the movie to defend the high school student who accompanied him on his recent journey during t a disciplinary hearing. This is a fun monologue to watch Pacino deliver!
Direct Address (to the Audience)
Jane B. has already mentioned that Saturday Night Live begins with the guest host giving a monologue at the beginning of every show, but this also applies to almost every late night show: The Tonight Show, the Craig Ferguson Show, the Conan O'Brien Show, The Letterman Show, etc. Each of these shows has a set up that allow the host to come out and speak (tell jokes) directly to the audience.
Other examples of television shows that used monologues to directly address the audience were Little House on the Prairie, The Wonder Years, and My Name is Earl, and Scrubs just to name a few. Each of these shows allows one or more of the main characters to editorialize what transpired via narration of varying lengths. This speech is directly solely at the audience.
Finally, in the play Macbeth by William Shakespeare, Lady Macbeth first begins a soliloquy directed at her absent husband, but this speech turns towards the "Spirits that tend on mortal thoughts," which is a sly reference to the audience watching the play!
I hope you found these examples helpful in understanding what a monologue is and the ways in which they can be delivered in film, television and plays.