Anime Fun and it Works
The Devil may Cry animated series is a lot like the games. Hugely over-the-top action with swords and guns, breaking the laws of physics for fun and profit, etc. Like the games as well, the plot of the overall arc was alright. Nothing awards-worthy, but enjoyable. Some individual episodes are very good, and they never go below "okay." They run the risk of Boring Invincible Hero with Dante, since he has Plot Armor for the games that happened after, but it is so crazy that I didn't mind as the series went on. Besides, they Lampshade the whole thing anyways saying that the games are Dante's toughest missions and this is about the challenge of what tends to go down between games.
Also like the games, the character of Dante is easily the best part. He and Patty are both very well written for themselves, moreso than the plots themselves or other characters. It does make the consistency an issue, but it's nothing too serious. As usual, Dante is a super XL Ham with a lot more to his personality than he lets on, and Patty is surprisingly a good addition considering that whole thing with adding kids to an adult story, and she works very well. Morrisson is well-written in his dialog but his personality isn't fleshed as much as it could and should be, I hope to see him in any future games.
So in the end it's a fun show to watch if you are already a fan of the series, if you aren't then maybe not. I sure as hell enjoyed it.
Anime Worth watching if you're a fan, but don't expect too much
To keep this as short and simple as I can, after playing through Devil May Cry 3, and then going to this, I found myself slightly disappointed.
Devil May Cry has always been about how awesome it is to be a demon hunting badass who goes through demons like a knife through butter, and in the series Dante continues doing this, but the big difference between this and the games is how unsatisfying it feels here. To be blunt, most fights Dante goes through are over in just a few seconds. In a game where this is the entire basis, watching just a few seconds of this every 20 minutes or so feels empty. Even the last 'boss' of the series. Literally one slash, a few words, one bullet and then it's over. Boom.
It does help establish the world of Devil May Cry a little, and Dante is mostly in character, still a cocky man with a love of pizza along with the addition of Strawberry Sundaes. But if you loved the games, just keep in mind that here, Dante is more of a Boring Invincible Hero than the Showy Invincible Hero he is in the games. If anything, that would be the strongest area of this series.