This. This this this this. I signed on for the first time in months just to recommend this but someone already did so I will support this. This is great sci-fi and crime drama, and has a good smattering of action as well.Nicholas Mendoza said:If you want a good sci-fi anime then you should watch "Psycho-Pass". It's about detectives solving crimes in a future Japan whose laws are governed by a robotic system, and later on tackles the problems of having that system decide almost all your choices in life. Below is a better summary of the anime if you're interested.
Summary:
In the near future, it is possible to instantaneously measure a person's mental state, personality, and the probability that a person will commit crimes with technology called the Dominator. Just thinking about a crime can make you guilty, and in this world there is no mercy for criminals. Detectives work in pairs--one Enforcer and one Inspector--with Enforcers delivering lethal justice, and Inspectors making sure their partners don't take things too far. The story follows Enforcer Shinya Kogami, who must solve and manage crimes in this dark future.
Someone mentioned Gantz. That is...not nearly so good a show, and extremely shallow and infantile, but has sci-fi themed action all over the place.
Daughters of Mnymosene is in a similar boat, but blends psychology and trippy pseudo-religious stuff into the sci-fi. If you wanted the boobs and gore that Gantz offers, this has even more. In fact, since it also has a better story, just watch this one.
Serial Expirements Lain isnt an action anime, but if you like the sci-fi that questions humanities relationship with technology (GitS, PsychoPass) it will serve you well. Trippy, and sometimes disturbing.
Technicolor robots are silly, but Eureka SeveN has lots of sci-fi action as well. And more depth than the silly robots betray.