The importance of this event is shown by the many ways we’re reminded of it.
In the Beit ha-Mikdash, during the Shabbat afternoon Tamid (perpetual offering), the choir of L’vi’im (“Levites”) sang the Shirat ha-Yam “antiphonally” (i.e. one part of the choir “calling,” the other part “answering” or “repeating”). 
In the annual cycle of parshiyot or sidrot (Torah readings), this is read during parshah “B’shallach,” which will occur (this year) next Shabbat (1/26). Unlike most other shabbatot, however, rather than the name being based on the title of the parshah being read (i.e. “Shabbat B’shallach”), it’s named “Shabbat Shirah” — because of the special importance of that particular part of the reading.
“Shirat ha-Yam” is also part of the special Torah-reading for the 7th day of Pesach (Passover).
In Torah, our attention is especially attracted to it because it’s written with a special calligraphic layout that’s often reproduced in chumashim (Torah in book-form, separated into the weekly readings) and even siddurim (prayerbooks).
It’s described as “half bricks over whole bricks” . I’ve also heard it described as “two columns [of water] through which the Israelites [i.e. the middle column] are walking.  The Talmud clearly specifies the style required to be used in the writing. 
There are other “songs of deliverance” in TaNaCh, too.
“[A ‘Shirah’ is] a song that proclaims the perception of the hand of G-d in the course of events.” 
The special calligraphic layout associated with “Shirat ha-Yam” — our oldest poem of deliverance — is also used for writing later “poems of deliverance” in TaNaCh: Mosheh’s song (D’varim 32:1-43), D’vorah’s song (Shof’tim/Judges 5:1-31), and Tehillim/Psalm 18. “D’vorah’s song” also forms part of the haftarah of Shabbat Shirah — the “deliverance” theme being re-emphasized by the repetition of the special calligraphic style employed by both. (If, as some historians say, the haftarot came into use during a period when Torah-reading itself was forbidden, then we can see an additional reason for reading “D’vorah’s song” on this Shabbat: the calligraphic layout is the reminder of that of “Shirat ha-Yam.”)
In the traditional liturgy, the “Shirah” is read daily at the end of the “P’sukei d’Zimra” section of the Shachrit (“morning”) service. When it’s read aloud, a special “nusach” or melody is used. [*]
The Shirah is important not only for what happened in the past, but for its resonance in our lives forever into the future:
“…in reciting the passages about ‘K’ri’yat Yam Suf‘ in our daily Morning Prayer, we do not merely recount that important historic event, but also reaffirm our trust in G-d.” 
Reading “Shirat ha-Yam,” we reaffirm that G-d’s “hand” is in all events; that G-d rules over nature itself; that G-d is able to do absolutely anything.
Then — we can trust.
(for continuation of discussion, see:
 Shemot/Ex. 15:1-18, followed by a shorter song sung by Miriam and the women (15:20-21).
Full text and translation:
 See JPS commentary, pp. 76-77; further citation needed
 Shabbat 103b; see also the footnote in the Soncino edition of that page.
Further, see: Kolatch, Alfred J.; This is the Torah; Jonathan David Publishers, Inc.; p. 113.
Megillah 16b — “All the songs (in Scripture) are written in the form of a half brick over a whole brick…”
 http://en.wikipedia.org/wiki/Song_of_the_sea; I’ve heard this elsewhere, too.
 Sofrim 12:10
 Hirsch, Rabbi S.R.; The Hirsch Psalms; © 1977 by Phillip Feldheim, Inc.; p. 116
[*] Siddurim (prayerbooks) with an extended commentary (e.g. the Hirsch Siddur) can be excellent sources of commentary on the Shirah, supplementing those found in chumashim (Torah in book/weekly format).
 Mindel, Rabbi Nissan; As for Me — My Prayer; Merkos L’inyunei Chinuch, Inc., 1975; p. 133