The Super Robot Wars franchise is chock full of these. One of the main reasons why the games are popular is also credited to how kickass the character Leitmotifs are.
First off, all licensed series have their openings and other music for its characters as their own Leitmotifs, thus they won't be listed here. Many of these are awesome in and of themselves, so see their relevant Anime sections for those.
"GONG" is one of the greatest songs ever made, both in terms of the melody's essence, as well as the context of the song in relationship to Alpha 3 it appears in. See the lyrics for yourself.
Although it can be argued that "Skill" in Alpha 2 is the most popular JAM Project song, used as finale of many of their concerts or used for an encore. Fans have made this powerfully clear in a number of animated music videos made over the years. One powerful example is during the final opening CG scene in Alpha 3, where the Alpha Numbers stare down an impossibly huge numbers of STMC, and charging towards and getting buried in an endless swarm of them. The actual music makes this scene look rather doomed and depressing, but overlaying it with the end of "Skill", however, and you absolutely cannot believe for an instant they aren't going to emerge victorious (or hold back the Manly Tears the end of that song forces from you).
The 3-episode Original Generation: The Animation may not have been great, but at least JAM Project provided "Meikyuu no Prisoner" ("Prisoner of the Labyrinth"), later used as its own Leitmotif in Original Generations and Original Generation Gaiden.
"Gate of Magus", Sanger's original theme from Super Robot Wars Alpha Gaiden, later adopted by Wodan Ymir, his Alternate Universe counterpart. The image of a desperate struggle between good and evil is conjured into the mind of the listener by the interplay of flute and organ music, with the exchange of blows represented through the cacophonous roar of trumpets and copiously ominous percussion.
Back in the day when Mazinkaiser was an SRW-exclusive unit, it didn't have the current Leitmotif from the OVA. However, Banpresto made an exclusive theme song for it. Here is the one used in Alpha 3, and this one a vocal version sung by Ichiro Mizuki of JAM Project.
"Messenger From the Void" from Alpha/Alpha Gaiden and "The Gun of Dis" from Alpha 3; although the latter may seem like a "laxy remix" of the former, the significance was mind-blowing back when Alpha 3 was released.
"Ware ni Teki Nashi" ("None Can Oppose Us") for the RyuKoOh/KoRyuOh in Alpha. You can simply feel the vibe of awesomeness from two reawakened mechanical gods in the form of a dragon and tiger, bringing justice against extraterrestrial invaders. Then there's its Alpha 3version for the Shin RyuKoOh/KoRyuOh, suitably epic for the final form incorporating all four gods. Its vocal version is even better.
"Twin Icon", the theme of the Nashim Gan Eden and by extension Irui.
So much attention is paid to "epic" tracks that the less glamorous mood music is always ignored, such as "What Lies Before The Struggle". Unlike more recent intermission music, this track manages to be solemn, yet full with resolve, and it's a shame it has not been used since Alpha/Alpha Gaiden.
For additional awesomeness, the vocal version used in episode 10 of The Inspector, as sung by the Latooni Subbota and Shine Hausen's voice actors. This is the first Leitmotif since the Alpha series to be given lyrics.
"Ouka Genei" (localized as "Cherry Blossom Illusion"), Ouka Nagisa's Leitmotif in Original Generation 2, brings to mind a bird soaring on the wind. In a way, it's almost heroic but her situation is an ironic one. This makes it more satisfying when she pulls a Heel-Face Turn.
Kurogane Arrange Music made a great version of it.
"Rail to the Dangerzone" and "Born to Fight", two generic Leitmotifs that can used around for all units. These days, both are considered extinct themes, yet most players might just relegate it to pilot Russel Bagman, the only character who doesn't have a character-exclusive theme.
The rallying themes from Original Generations and Original Generation Gaiden. When it looks like the enemy's about to win, these songs kick in at the last minute and the characters get a Heroic Second Wind. Added to this, some of these are previous SRW themes, and get used in the final episodes of The Inspector. For example, "Machine Soul" and "Go!" are taken and reorchestrated from Super Robot Wars Impact.
One of the great things about Original Generations is it gives exclusive Leitmotifs to almost every playable character on the roster without neglecting their presence, ranging from "Treue" ("Loyalty") for the Blue Blood Leona Garstein, "Rushing Dandy" for close-quarters combat Ace Pilot Kai Kitamura to "Hero Senki" ("Hero War Chronicles") for the enigmatic Gilliam Yeager. Even Inspectors' leader Wendolo gets the unique "The Judge and the JudgedLeitmotif rather than the usual "Violent Battle" theme the other Inspectors have.
In the same vein as "Ware Koso wa Baran Doban" and "Makenaize! Gunleon!", the Second Original Generation brings us "Gantetsu Banchou G Bankaran no Uta" ("Song of the Iron Stubborn Gang Leader G Bankaran"). Absolutely NO ONE saw this Leitmotif coming, particularly from a Japanese Delinquent who got little more than a mention from a drama CD.
One Leitmotif given an awesome guitar riff is "Genocide Machine II", used exclusively for Guest general Grofis Lacrein, a remix of the old "Genocide Machine" from 4 and its remakes.
Not only do the JakuOhKi and BuOhKi finally make an appearance in the games via the Second Original Generation, we're treated to their Leitmotif"Jakubu Shuuten" ("The Phoenix and Tortoise Encircling the Heavens").
Once "Ultra One" starts playing, you've realized you played right into the hands of the Bigger Bad for the Second Original Generation. If you listen carefully, you'll hear it incorporates parts of "Arrow of Destiny" from Alpha, a key to the identity of this Bigger Bad.
"Dark Prison", Shu Shirakawa's Leitmotif has remained pretty consistent throughout the franchise. Everyversion always delivers the ominous feeling of what kind of person Shu is: a Magnificent Bastard kept imprisoned of his own free will for so long, his release WILL spell doom on those who manipulate him.
"Hakugin no Datenshi" ("Platinum Lucifer"/"Fallen White Knight") Excellen Browning's Leitmotif. A cheerful, energetic piece, you are now picturing Excellen in a cheerleader's uniform. Impact version here and Original Generation version here.
Doujin remixes of are relatively few and far between, but some are great in their own right. Check out moAbi's version of "Steel Beowulf".
"Kurenai no Shurashin" ("Crimson God of Carnage"), Leitmotif of Folka. One of the better tunes in Compact 3, it turned more awesome when it appears in Original Generation. You can practically feel the vibe that Folka truly is Kenshiro incarnate piloting a Humongous Mecha.
When this game was released, none of its original musical tracks were named. Once the Second Original Generation was released, the title theme was given the name "Destinies". It was given an orchestrated version for the Second Original Generation.
Joshua and Cliana each have a normal Leitmotif, but a second one is triggered whenever they use the strongest attack in whichever mecha they are in. For Joshua, "Desire" and "Drumfire", respectively; for Cliana, "Duologue" and "Duet", respectively.
"Devastator", the default theme of the Melior Esse of the Ruina.
"Despair", DestinyBig Bad Perfectio's Leitmotif. Until the release of the Second Original Generation, fans have been calling his theme "King of Ruin". Its remix from 2nd Original Generation is also pretty great.
"Determination ~ Pride and Memory in the Heart", the Leitmotif used when Kazuma's younger sister Mihiro gets to pilot the Valhawk solo for one scenario (for the rest of W, she's a co-pilot). It's gentle enough to match a character like Mihiro but forceful enough to match what she's capable of handing out, even worth keeping on the Valhawk when Kazuma returns post-Time Skip. It's kept on the Valstork battleship, so you'll hear it by using the eldest Ardygun sibling Shihomi, after she succeeds their father Blessfield. This possibly makes this Leitmotif the Ardygun family's theme song.