The wonderful short songs instrumental that give each series of Digimon its unique mood (rock, classical, flute, jazz, etc.) feature in the Uta to Ongaku Shuu albums (two per series until Digimon Savers). Below are some links to listen the long(er) songs directly, but before, a link (with commentaries, but lots of loading) to a flipping good fan-made English translation of the first through fourth and the sixth Japanese openings (or, to simplify things, every pre-Xros Wars Kouji Wada theme), brought to you by these guys. Oh, if only (just video).
The "Strong Version" of Butterfly is probably one of the most epic things you will ever hear in your life!
Maasaki Endoh's take on "Butter-Fly" again adds awesome to an already amazing song. Or, for the most acurate piano version so far. It really demonstrates the complexity of the full songs, as anyone that tried playing digimon songs in guitar hero knows.
The two ending themes in their full version qualify:
I wish, the first theme, sung by Mimi's voice actor, Ai Maeda.
Keep on, the second theme, as sung by AiMnote Ai Maeda's name as a singer. She also goes by "ai" in her capacity as a songwriter..
The instrumental piece in the Japanese version that tends to be played during Moments Of Awesome (Venom Vamdemon's defeat and the first appearances of Magnamon and Quinglongmon in 02, to mention a few) deserves recognition.
Shouri ~Zen no Theme~, a strangely simultaneously eerie and beautiful track used to excellent effect in the last scenes of episode 21.
The never released Digimon version of Concierto de Aranjuez - it plays only at three points in the anime, and was never officialy released, but each time it plays, it's awesome. First time it plays, the children and Leomon are going to mount Mugen to face Devimon, the second time is when Yamato is tricked by Cherrymon, and the third, most memorable time, when Angemon evolves into Holy Angemon.
"Bokura no Digital World", a memorial song for the first two seasons: all 24 starring cast members, the narrator, and the opening and ending song's performers.
Break Up! (yes the exclamation point is part of it) comes out in the top.
Here We Go. The little, 5-second version that plays when they enter the digital world is awesome, but the longer version is EPIC.
So epic they HAD to use segments of the longer version in the dubbed version of the movie! (when Wargreymon and Metalgarurumon head into the internet to battle Diaboramon despite the fact that they had severe battle scars...it is truly epic!)
Most of the Image Song collections for the characters are certainly worth listening to, although Daisuke's and V-mon's are really about how awesome they are. Fast forward a year, when the Natsu e no Tobira CD Drama (The Door to Summer) comes out, yankingpoor Daisukeup anddown thewhole damn street. The Narrative of the CD Drama is interspersed throughout with songs from the various characters, and Daisuke's occurs at The Climax. Reach For You showcases that Daisuke has grown up a fair bit (he's no longer singing off pitch); and hoo, boy, it shows.
Another good Daisuke song is his 10th Anniversary Special: "Ashita". Much more cheerful than "Reach For You", and much less depressing than "Natsu e no Tobira".
Digimon Tamers had plenty of great songs. Some only heard in the anime, like the sad but incredibly moving Saxophone with piano background version of The Biggest Dreamer, and some that were never even heard in the anime, and that (obviously) were never sold around the world.
Rika's theme from the Best Tamer album, Moon Fighter, that firmly established her as a Badass.
Pretty much any moment where the Ultimate/Mega Digimon appear is made instantly awesome by that song. It also helps that the 3 different Digimon get different renditions to start up. Gallantmon goes straight into the rock chorus of the song, MegaGargomon starts up with the rock riffs from the beginning, and Sakuyamon gets an entirely different theme (More Traditional Japanese sounding) before going into One Vision.
the German version is almost even more awesome for using the song's iconic badass guitar solo right at the beginning of the song.
"Yuuki o Uketsugu Kodomotachi e" is another memorial theme, this time for the end of Frontier, and featuring darn near everyone who ever recorded a theme song or battle theme for Digimon up to that point.
Then there's "The Last Element", which played in Frontier as the Hyper / Unified Spirit Evolution theme (in other words, for Emperorgreymon y Magnagarurumon), and during the birth of Susanoomon. The track which replaced it in the dub is just as good.
On a more solemn note, Theme of Darkness ~Kouichi's Theme - while the other "Theme of ____" BGM tracks are instrumental arranges of their respective characters' image songs, Kouichi's is a slow arrange of Kouji's "Theme of Light".
The most hilarious song ever in Digimon, Get the Biggest Fire, where the two main characters of Digimon Frontier try to sing a new theme, starting with the earlier themes. They sing very badly.
Frontier's opening sequence "Fire" is so fun and uplifting. The English opening is really catchy and powerful too, to say the least.
The entire BGM to the dub, composed by Thorsten Laewe.
This series takes lots of inspiration from mecha animes such as GaoGaiGar, and as such it brings loads of hot blooded music to the table with it! To begin with, "We Are Xros Heart" by the magnificent Kouji Wada continues the Digimon tradition of seriously kick-ass evolution themes. Also dubbed "the ending theme" by fans, since the show has no real ending credits, and this song has a tendency to show up at the end of the episodes, usually during Moments of Awesome.
The DigiXros-theme, which tends to play immediately before "We Are Xros Heart", is quite cool too.
Kiriha gets his own theme music as well, complete with lyrics that describe his blazing blue flames perfectly, Blazing Blue Flare. Makes any moment of the series where he's kicking ass all the more awesome, usually always with Metal Greymon.
And just when you think you can't get any more awesome, Mr. Kouji Wada goes and gives us "X4B The Guardian" for ShoutmonX4B's appearance. Xros Wars seems to be giving its main Digimon their own themes.
Not just the good guys, but the evil Digimon get their own themes too! Dark Knightmon has Dark Knight ~Immortal Champion. With lyrics like KILL YOU in it, you just know it belongs to a magnificently evil bastard of a villain.
The pattern continues with "Dancing Hero of the Skies! X5!", which sounds like something straight out of a Super Robot anime! (Complete with lyrics describing the transformation and abilities of Shoutmons new form!)
Now that evolution has been introduced, even more awesome songs are sure to follow, the first of which is Taiki's evolution theme, Evolution and DigiXros Ver. Taiki, perhaps the epitome of Hot Blood condensed into a single song, this brings Kouji Wada's songs for Xros Wars to four, which is his highest yet for a Digimon series, equal with Frontier. And he didn't even sing the Opening theme!
Speaking of the opening, Xros Wars changed OP's for its second arc, so behold New World, the first Digimon Opening sung by a female singer. Its chorus leaps straight into earworm territory.
The instrumental music in the series merits mention as well. Fight for Victory plays in some pretty tense moments in the series.
And if you thought they couldn't top what they already had, they give us We Are Xros Heart - ver. X7 , sung by a seemingly impossible TRIO of Koji Wada, Takayoshi Tanimoto, and a returning Ayumi Miyazaki! Not to mention with this, Kouji Wada has sung a total of five (six if you count his small part in Kiriha's evolution theme) songs in Xros Wars, making it the most Kouji Wada songs in a single Digimon show!
There's also "Nakama No Tame Ni". It generally plays during some of the bleakest moments of the series. Highlights include a time when Tactimon holds Akari and Zenjirou hostage in exchange for the Xros Loader and when Taiki is facing down Bagramon himself with no backup except Akari and Cutemon.
Xros Wars: Young Hunters
"Tagiru Chikara" (which can translate to either "Tagiru's Power" or "Overflowing Power") is a serious contender for the rockingest song Digimon has produced. Besides being used during evolution-related moments of awesome, it's sung by Psychic Lover. Need we say more? You can find it right here.
"Shining Dreamers" is Yuu and Damemon's evolution theme. Shame it was so underutilized in the show proper, because it's really good.
"Legend Xros Wars" is an epic tribute to all the seasons of Digimon thus far, featuring references to all the theme songs in its lyrics. It's used in moments with all the heroes coming together, like the battle between all the leaders and Quartzmon's army of VenomMyotismon and MaloMyotismon. WE ARE LEGEND HEROES!, indeed.
Requiem from the first movie's finale. It may not be as fast-paced as most of the other songs here, but it easily matches them in sheer levels of awesome.
Not only did that song make Omnimon/Omegamon's first appearance truly epic, but it also made Imperialdramon Paladin Mode's appearance epic (That's movies 2 and 4). Also, in the strangest of places, the song was used for Mercurymon's opera style battle with Takuya (Digimon Frontier). Watching a main hero get beaten to death with this music only makes the scenes more awesome and symbolic.
From the Digimon Adventure pilot movie, where it all started: we are treated to the short version of Butter-Fly, with Kouji Wada singing a cappella at the beginning. It's incredibly powerful.
Note that most Digimon games have different soundtracks depending on whether it is the original Japanese version or an English translation; one of the most common changes is the removal of themes based on songs from the anime, though they never put equivalents from the dub in.
The Japanese version of Digimon Rumble Arena features instrumental covers of the Japanese openings and inserts up to that point (save The Biggest Dreamer, which was its opening theme in its original form). They're all fantastic, with Butter-fly expectedly being a standout.