DP inspired a whole sub-genre of young female fighting duos, typically in the age range of 17 to 19 in older anime, and younger in more recent series. To cover everything would be difficult and very extensive, so I won't even pretend to be complete. What we'll look at here are some of the more immediate responses to the Lovely Angels, including some pretty obscure ones.
Probably the most immediate reaction to the DP anime, Wannabes was released in December of 1986 as an early AIC effort. Miki (left) and Eri (right) are two aspiring woman pro wrestlers (as the name of the team and the OVA would imply) who are drawn into a conspiracy involving a muscle-strengthening designer drug. The story goes to the root origin in pro wrestling of DP itself; the theme of such a drug recurs in the DP anime -- TV episode 4 and OVA episode 7. Unfortunately, the plotline of this story is pretty weak and Wannabes is largely forgotten today. Sonoda Kenichi was the character designer and was clearly drawn to the concept of fighting female teams. He next executed the designs for the Garu Fuoosu <Gal(l) Force> series: Kakinuma Hideki's manga started earlier in 1986 and was chosen to be adapted for animation after scarcely four months in print. From there, Sonoda was involved shortly afterward in the character design for the '80s Bubblegum Crisis OVAs and soon commenced his own long-running manga series, Gunsmith Cats. Rally Vincent and Minnie-May Hopkns are also evidently conceived under DP's influence.
Takahashi Rumiko's interaction with DP, which goes back to their print stories early in the 1980s, chiefly displayed in Urusei Yatsura, is discussed elsewhere in this site.
By 1990, the number of "bluehead-redhead" duos who bore something of the mark of Yuri and Kei had proliferated greatly, appearing in series as varied as Ikkiman, Dangaiou, and Cyber Formula Zero.
An interesting example during the transition between "old-school" anime and present practice is the 1989-90 Sunrise series Juushin Raigaa <Beast God Ryger>, where we meet the supporting characters Mai (left) and Yui Koujiro (right). They may have served as something of a "jumping-off point" for the later DPF character design ideas developed during 1993 by the doujin circle U.G.E. Connection, which included Kimura Takahiro.
Incidentally, the image of this poster from Newtype, which has appeared elsewhere on the 'Net, is generally misidentified as a Dirty Pair poster; these young ladies are, in fact, Yui and Mai.
Hikawa Reiko's Gude Crest was developed as a one-shot OVA in 1990, animated by J.C. Staff. Itinerant princesses in search of adventure, Efera (left) is the level-headed sorceress, Jiliora (right) the crude, hot-tempered warrior. The characters are voiced by Matsui Naoko and Ikura Kazue, respectively, who also sing the end credit song; their portrayals leaves little doubt about the inspiration for these characters. The character designer was Dokite Tsukasa, using a style similar to that in his work for DP's Conspiracy of Flight 005. [This OVA is the stated inspiration for Ryan Mathews' well-known Internet DP fanfic, The Game Eternal.]
Even without the specific allusions through character design, the "DP concept" remains very influential in female protagonist duos in manga and anime, such as Natsumi and Miyuki (You're Under Arrest), Miyu and Maika (Hyper Dolls), and Fam and Ihrie (Ruin Explorers). Even within larger character ensembles, it is still common to have two closely-bonded, though sometimes rivalrous, young women with contrasting personalities. We can yet see echoes of Kei and Yuri in such pairings as Esmeraldas and Maetel, Haruka and Michiru, Rei and Asuka, Chocolat and Tira (Bakuretsu Hunters), Lina and Naga, Shayla-Shayla and Afura Mann (El Hazard), Cherry and Bloodberry, Janny and June (Sol Bianca), Ryoko and Ayeka, Meryl and Milly, Excel and Hyatt, Mireille and Kirika (Noir), Eclair and Lumiere, Yao and Lu (Miami Guns), Nagisa and Honoka (Pretty Cure)/Mai and Saki (PC Splash Star), and others. [A tip o' the virtual hat to Psyber Raven for suggesting many of these.]
Daughters in the realm of gaming