This anime is really fun and cool, and if you like your anime with some sci-fi, a mysterious hero and some very silly moments and humor, "Dimension W" is for you.
We have the typical hero that has a secret and, even if he doesn't want to, has to join forces with another character. In this case, our hero is a 'collector', a person that tries to recover illegal components that use energy from the 'dimension W', a dimension that has helped humanity to get an endless supply of energy. He is old style and doesn't like the use of the components that let humanity tap into the dimension W. Not very deep sci-fi, that's true. At the very beginning of the anime he gets involved with a robot, the creation of the man that found the dimension W and the robot (with the typical character and looks of a young girl, something too typical in some kind of Japanese anime) decides to stay with him.
From that moment one we get our hero, Kyoma, getting his missions and the robot Mira helping him. The model is one mission per episode. Around the half of the series we get into the big arc of the show that will last till the end of the anime.
The first part is lots of fun, with cool characters, great rhythm and funny plots, with some silly humor thrown into it. The second part is darker, the plot gets a little bit messy and is more into 'big fights' but it is still really interesting and fun. Not very demanding, but always fun.
The animation is really cool, even if there are a couple of moments where the quality is not great. It does a great job in making the viewer feel involved in this world and characters, with a very stylized look and a nice use of color. Perfect for this type of series. And the music is just plain great.
P.S.: I haven't watched the OVA, so this review is just for the anime series.