Rava said: One is required to become intoxicated on Purim until the point that he cannot differentiate between 'Cursed be Haman' and 'Blessed be Mordechai.' (Gemara Megillah 7b)
Why is inebriation on Purim halachically mandated? Do other forms of celebration not suffice to express our joy at the salvation precipitated by the nes of Purim?
The story of Purim is unique in that each segment of the tale appears to be a coincidence that is often unrelated to the balance of the narrative. Hashem's Name does not appear in the text of the Megillah, and the miraculous nature of Purim is detected only by piecing together all of the events and realizing that each occurrence was a purposeful piece in Hashem's puzzle; it was the Divine's grand scheme for bringing B'nei Yisroel near to Him and saving them. The miracle of Purim occurred via Hester Panim, which means that Hashem interacted with the world in a hidden, imperceptible manner. (The custom to adorn masks and costumes on Purim [v. Remo in Shulchan Aruch O.Ch. 696:8] bears recognition of this, for we celebrate Hashem's salvation via Hester Panim, in which His involvement with the world was masked from open view.)
In this same vein may we understand the halachah of drinking on Purim. The Gemara in Eruvin (65a) explains that one's hidden, inner essence emerges as a result of alcohol. Inebriation reminds us that one can appear to be a certain way on the outside, whereas that same individual is totally different internally. By merrying on Purim through the medium of drink, we celebrate and recognize once more Hashem's nes via Hester Panim, as we reflect upon Hashem's miraculous acts through his Hidden Presence, acting behind the scenes rather than overtly.
The Arizal stated that Yom Kippur and Purim are related ("Yom kePurim" - "A day like Purim"). On Yom Kippur, we return to Hashem and are represented by the Kohen Gadol, who enters the Kodesh Ha-Kodoshim - the most inner sanctum of holiness - which is removed and off limits from day-to-day life. We shed our material, earthly shell and identify ourselves as malachim (angels), relating to Hashem via our inner essence, our neshamah. This is the parallel between Yom Kippur and Purim, for both of these days compel a realization that our inner, spiritual, Godly selves be recognized and flourish beyond our exterior facade so as to draw near to Hashem.
On a halachic note: The Gemara (Megillah 7b), Rambam (Hilchos Megillah 2:15) and Shulchan Aruch (O.C. 695:2) indicate that drinking on Purim is a component of se'udas Purim, the Purim meal. Furthermore, the Remo in Shulchan Aruch (ibid.) writes that one's drinking on Purim is supposed to be "l'shem Shamayim" - for the sake of Heaven (rather than as an act of pure indulgence). It is thus evident that those who drink large quantities at night after the Megillah is read as well as on Purim day before or after the se'udah are acting quite inappropriately, as their drunkenness is not in the context of mitzvah performance and is a deviation from the intent of Chazal. Such conduct, aside from often being quite dangerous and constituting a massive chillul Hashem, is an outright distortion of the most holy and sublime message of Purim.