EDIT JULY 2019: I've now realized that Robin is definitely Dick Grayson in this series, but I'm still going to leave this how it is just to highlight my stupidity.
Robin is Dick Grayson, NOT Tim Drake. Although, this version of Robin was definitely heavily influenced by Tim Drake, but he IS Dick Grayson.
My Stupidity :P[]
I know pretty much everyone on this site is settled with Robin being Dick Grayson, but it was never truly confirmed in the show itself who he was.
I personally think Robin is Tim Drake in this series.
Reasons why
Robin himself: His personality is mostly based on Tim, as Tim is the one who is known as the more serious Robin, while Dick Grayson was the more light-hearted and optimistic Robin, Tim, much like the Teen Titans Robin, is also known to be pretty obsessive when it comes to taking down villains, his costume and weaponry are also more associated with the Tim Drake version of the character, in the comics Tim was the one who primarily used a Bo-Staff, in recent years various Robins have been shown using a Bo-Staff, most notably Dick Grayson and Damian Wayne, but at the time it was mainly associated with Tim (still pretty much is to this day).
The Flying Graysons scene: In the comics, Tim was in the audience the night Dick Grayson's parents died, him having seen The Flying Graysons' performance would eventually lead him to discovering Batman and Robin's true identities, as he saw Robin do a quadruple somersault, which was only done by one of The Flying Graysons.
The Oath: In Dick Grayson's first appearance, Batman made him take an oath to always serve Justice, when Raven enters Robin's mind in the episode "Haunted" she passes by Shadows of Robin and someone else (possibly Batman), in a scene that looks like Robin, with his hand up, taking some sort of an oath, doesn't really mean he's Dick Grayson, as it's safe to assume that Batman would make all the Robins take this oath.
Nightwing (possible future): Apparently there was a comic panel (featured in a Lobo comic) which showed an alternate future with some big muscular dude in a Nightwing costume, his name was revealed to be "Tim", so it wouldn't be the first time Tim was shown as Nightwing.
Larry the Titan (Nosyarg Kcid): Most likely just a gag, according to David Slack it was mainly just to keep people guessing, which you could take as doesn't necessarily confirm that Robin is Dick Grayson, or maybe it does, he said he's not telling, Larry is from an Alternate Dimension after all.
Teen Titans Go! #47: Spin off Comics, such as this, are usually of questionable continuity, much like many of the DCAU Batman comics, there was one that showed a completely different version of the DCAU Superman (though that was released before Superman: The Animated Series came out), also a few issues of Teen Titans Go! contradicts the series, such as some of the Terra issues and Cyborg's origin, in the comic it showed his mom is alive, however in the show it's implied she's dead, on Cartoon Network's YouTube channel they released a video about Cyborg's origin in Teen Titans GO! and the original series, on the original series part it states that his mom died during the accident that led to him becoming Cyborg, so the Go! comic series is probably nothing to go by.
Jason Todd: A majority of the Teen Titans fanbase (including Beast Boy) believe that Red X is Jason Todd, but it doesn't really matter if Red X is Jason or not, in the episode "X" a picture of Jason as Robin was shown, and in the New Teen Titans short "Red X Unmasked" Jason was mentioned by name, if Jason has been Robin by that point, then Dick Grayson would be Nightwing, but those could have most likely just been gags as well... or maybe they do mean something (I still think Red X is Jason Todd).
Robin and Starfire: In the comics Dick Grayson was the Robin who fell in love with Starfire, however for this series it's quite possible they had kept the Robin and Starfire romance without reverting Robin back to Dick, as for the ages, Teen Titans is possibly one of the first (if not THE first) instance of major character age changes, plenty of other TV shows had done something similar, most notably Young Justice, which made Dick Grayson and Wally West younger than Superboy, Miss Martian, and Aqualad (Kaldur'ahm).
Team Line-Up: The team in the series is mainly based on the 1980s New Teen Titans line-up which had Robin (Dick Grayson), Starfire, Cyborg, Raven, Beast Boy, Kid Flash (Wally West), and Wonder Girl (Donna Troy), however in 2003 a new series was released and the line-up featured Robin (Tim Drake), Starfire, Cyborg, Raven, Beast Boy, Kid Flash (Bart Allen) Wonder Girl (Cassie Sandsmark), and Superboy, unlike Dick Grayson though, Tim was not the leader, but Tim would become leader of the Titans later on, the 2003 TV series may be the reason for the 2003 comic line-up as well as Tim eventually becoming the leader.
Robin vs. Deathstroke: In a similar manner to the Starfire issue, they probably just kept the Slade being Robin's arch enemy thing without reverting him back to Dick, but Dick was not completely obsessed with taking him down, Robin in the series however, was, this was probably done to highlight his obsessive personality, and like I said before, his obsessive personality is more similar to Tim Drake.
Official Website Bio: In 2008 the official DC website, DC HeroZone, featured a section called "Secret Files" and featured the DCAU versions of the Justice League, and the Teen Titans TV series versions of the Titans, and a few other characters. On Robin's page it confirms him to be Tim Drake, you could say it was probably just a mistake, since the other bios made some minor mistakes as well, but this most likely was not one of them, as there was a separate page for Dick Grayson, as Nightwing. That website was later revamped as DC Beyond, and the secret file section was removed, however the new site would refer to the Teen Titans version of Robin as "Robin III" and it stayed that way for a number of years, why not just call him Robin? Why add III, they most likely did that to let us know this is NOT Dick Grayson. I know a lot of you are probably going to be like "it's just some old stupid kids site, who cares" but the fact is, it is still an official Warner Bros. owned website, and they purposely used the Teen Titans Robin for Tim Drake.
Glen Murakami, the creator of the series, said this in an article from Cinescape Magazine "In my mind, it's Dick Grayson just because that's what I grew up reading in the comic, but I think continuity-wise it might not make sense to people because if it's Dick Grayson then it's Like, 'Oh, well, when does this take place in the Batman animated series?"
Then from an interview with one of the producers on the Divide and Conquer DVD, the only Robin he mentions is Tim Drake, he said this "The current Robin is a character called Tim Drake" but he could have merely been referring to who is the current Robin in the comics at the time, I don't know.
But this is just what i think, if you don't agree, thats fine. But please be respectful, no need to be an ass.
Maybe he is Dick Grayson, won't really know until the creator of series, or one of the producers, state something, with Teen Titans Season 6 possibly coming, maybe something might finally get confirmed... or maybe not due to the box office performance of Teen Titans GO! to the Movies.
EDIT: Teen Titans GO! vs. Teen Titans also didn't help with a sixth season getting made, but maybe that's for the best. If a sixth season DID come out, it probably wouldn't be like the previous ones, it would probably be terrible. Or maybe it could have been good. WHO KNOWS? Its still not happening...