The Bechdel Test: Passed on two occasions. The first is in Devil May Cry 2 between Matier and Lucia when the latter is distraught about her real origins, but Matier reassures her that the value of their history and experience is far greater than the circumstances of Lucia's birth. The second time is during the last cutscene of Devil May Cry 4 as Trish and Lady are excited about their next job of demon hunting.
Development Gag: Dante's alias, Tony Redgrave, likely serves as one to DMC's history as one of the many RE4 prototypes; the version that was retooled in the original game featured a protagonist with superhuman abilities spawned by biotechnology named Tony.
Uncle Dante - Dante, thanks to his in-game portrayal and relationship with Nero. note Which wouldn't be too far from the truth if one accepted details that were cut out from the final product and the novelization.
When coupled with the plethora of similar character traits, this led to the Fan Nicknames of Ichigo (Nero), Bankai (his Devil Trigger), Getsuga Tenshou (the shockwaves emitted upon DT-ing), Orihime (Kyrie), and Bleach May Cry (the game itself, as noted above).
No Export for You: A good amount of artbooks that goes into further details on things that got left out and the two-volume novelization of 4, Deadly Fortune.
The Other Darrin: Dante's voice actors. They didn't bring one back for a second game until 4 (see the Characters page for the full list). It wasn't until Reuben Langdon (Dante's Ink-Suit Actor) voiced him in 3 that a VA stuck. Subsequently, Langdon went on to reprise his role in 4 and The Animated Series, the latter causing a massive moment of fandom rejoicing when announced.
This is made even more jarring if one considers Dante's appearance as a Secret Character in the PS2 version of Viewtiful Joe. Although it came out a year after 2 (where he was voiced by Matthew Kaminsky), Dante's voice actor is the same as the original game (Drew Coombs). In other words, it went from Drew Coombs, to Matthew Kaminsky, back to Drew Coombs, and then finally to Reuben Langdon, who has been voicing Dante ever since 3.
This doesn't even factor in Dante's other out-of-universe appearance as a Guest Fighter in Shin Megami Tensei: Nocturne, where Dante's voice actor is Kaminsky again (however, it's just a case of reusing his grunts and warcries from 2).
Dante was Darrin'd again for the reboot, this time being voiced by Tim Phillipps. Granted, that Dante is technically a different character with a different personality, so keeping the same voice actor would have been odd.
Trish was voiced by Sarah Lafleur in the first game, Luci Christian in TAS (Atsuko Tanaka in the original Japanese version), and then Danielle Burgio in 4 and MvC3 (with Tanaka reprising in Japanese).
It would seem that out of all of the recurring characters (what few there are), only Lady has kept her VA (Kari Wahlgren).
Throw It In: The enemy juggling mechanic was born from a glitch that accidentally allowed juggling in Onimusha. The glitch was fixed before Onimusha's release, but was so Crazy Awesome that Capcom added it to to the original DMC.
Arkham was originally going to go by the name of Hyne (pronounced "Hai-neh"), but Reuben Langdon (Dante) didn't think it would work in English and convinced Capcom to change it. His alter-ego Jester was also named Joker early on in production.