Image text: Also, I apologize for the time I climbed down into your world and everyone freaked out about the lesbian orgy overseen by a priest.

Flatland is a short story by Edwin Abbott Abbott. Yes, that is really his name.  In Flatland, women are represented by lines, and the more important a man is, the more sides he has.  The least important male would be a triangle and the priest, in Flatland, has so many sides, he looks like a circle.  So, the image text is a reference to how an xkcd stick figure would look to the members of Flatland.  The text for Flatland is on Wikisource here, if you feel like browsing on your Wednesday morning.

Miegakure is an actual game in development that will allow the player to move in 4 dimensions.  The website is here, with a screen shot that looks eerily similar to panel 2.

And if you didn't realize, Spongebob is a reference to Spongebob Squarepants, the Nickelodeon cartoon about a sponge named Spongebob.  Spongebob is a square (as his name implies) - so that is why the character in the comic is able to draw arms and legs on the square to make him look like Spongebob Squarepants.

Image text: Using a ring to bind someone you covet into your dark and twisted world? Wow, just got the subtext there. Also, the apparently eager Beyoncé would've made one badass Nazgȗl.

The song playing in this comic is "Single Ladies" by Beyonce.  Which apparently had one of the best videos of all time... Anyhow, Gil-Galad was the last high king of the Noldor in Middle Earth.  Galadriel was a queen of the elves in Middle Earth.  Eru was the one god of Middle-Earth who created the Elves and Men, and Aule created the Dwarves, but Eru eventually approved Aule's creations.  So, he sort of created the Dwarves as Eru was the only god to give a spirit to a being, as he did with the Dwarves.

The character in the beret is apparently the bartender in a bar that Sauron frequents.  In the comic, Sauron upon hearing the song by Beyonce in the bar, has the idea to create his magic ring plan which presents the plot of the Lord of the Rings triology of books and movies.

Image text: I was going to be a scientist, but that seems silly now. Magical worlds exist. I've learned a huge truth about our place in the universe. I'm supposed to care about college? I mean, FUCK.

The main character won't just spend the next 70 years with his loved ones suspecting he is crazy.  Everyone will suspect he is crazy.

Image text: Moments later, the White Witch rolls up and, confused, tries to tempt the probe with a firmware upgrade.

This comic is a reference to the book The Lion, The Witch and The Wardrobe by CS Lewis and later made into a movie.  The children in the book are playing "hide and seek" in an unfamiliar house when one child hides in a wardrobe.  They then find a entire world known as Narnia behind (or inside) the wardrobe.

The comic is making a play on the Narnia tale, by instead of the child exploring the new world herself, she sends a probe.  This is similar and possibly a reference to the probes that NASA deploys to gather information about new worlds.  It also may be a reference to Stargate, in which the Stargate Command sends a probe to new worlds to gather information about the world.

EDITED TO ADD: The title appears to be a reference to the fact that the child in the comic does not run blindly into the new world, like in the book, but instead she deploys the probe to gather information first, which would be seen as "prudent".

(You absolutely have to click on the image to see it larger.  It is quite detailed and impressive.)

Image text: In the LotR map, up and down correspond LOOSELY to northwest and southeast respectively.

Lord of the Rings is pretty self-explanatory if you have seen the movies based on the series by JRR Tolkien.  It is important to note that the chart is based on the movie, not the books.  Second, is the original Star Wars trilogy.  If you haven't seen those, stop what you are doing right now and go get them.  Third, is the original Jurrassic Park movie.

The joke in 12 Angry men graphic is that in the movie all 12 jurors are all in the same room the entire movie.  They never move and they all always interact with each other, hence their lines stay straight and close to each other.

The last box is a movie called Primer from 2004, which became a cult classic.  It is about accidentally discovering time travel.  The plot is so convoluted and mixed up with the time travel between the original person and the so-called time travelling "double" that it is almost impossible to figure out where each character is at one time...as the comic illustrates.

UPDATE: These charts are roughly a reference to the map by Charles Joseph Minard that details the movements and losses of Napolean's troops on his failed conquest of Russia.

Example can be found here.

Image Text: Dear Peter Wiggin: This letter is to inform you that you have received enough upvotes on your reddit comments to become president of the world.  Please be at the UN tomorrow at 8:00 sharp.

This comic references the Orson Scott Card novel Ender's Game.  [SPOILER] In it, Ender's higher-than-average intelligence siblings, Valentine Wiggin and Peter Wiggin decide to make a move for power on earth by posting contrasting opinions of the Formic War on their version of the internet.  They used the pseudonyms Locke and Demosthenes respectively and eventually coerced the trust of the entire planet by playing their posts against each other.  This lead to Peter gaining control of the free world.

[EXTRA SPOILER] Peter is a borderline sociopath and kills that squirrel.