SixShooterOutlaw

*Cracks knuckles* Okay, here we go... First off, let us get the ultimate recommendation out of the way. Cowboy Bebop. If anime could be likened to a drug, then that is the ultimate gateway drug. Other classics that might interest you are Outlaw Star and Trigun.

Now that that is out of the way... Detective shows... There are a few... Detective Conan (localized as Case Closed) is probably the most popular, but it is rather long and can get predictable. Kindaichi Case Files is basically the same for older audiences. Recently there were two good ones called "Beautiful Bones: Sakurako Investigations" and "Everything becomes F: A Perfect Insider." Kind of on the same vein, one of my personal favorite animes of all time is Naoki Urasawa's Monster (a psychological thriller). I also rather enjoyed Hyouka.

Also along that line would be Ghost in the Shell:SAC and Psycho-pass. 

Moving on from that... if you like Transformers, you might enjoy Gundam series (Wing is the most popular) as well as other Mechas (RahXephon comes to mind for some reason). I highly suggest you look into synopsis before you pick up any of them though as they vary wildly and aren't always good. Reviews and impressions are crucial if you are going to delve into this. Oh and Big O (another classic), which basically combines batman with big robot fights.

If you like racing (which I garnered from your enjoyment of Forza) Initial D is about street racing. I enjoyed it but it isn't for everyone.

Space Battleship Yamamoto is fantastic sci-fi. Steins;gate is possibly one of the best time travel stories I've ever seen bar none. Summer Wars is basically the second Digimon movie done right. One Punch Man both pays tribute and pokes fun at superheroes. Jyu Oh Sei is also a pretty decent  sci-fi show as well.

Other shows offhand that I'd recommend just because they are just awesome or fun:
Fullmetal Alchemist: Brotherhood
Lupin III (fun anime imho but not for everyone) (Great grandson of Arsene Lupin gets team and steals stuff while pursued by Interpol agent)
No Game No Life (if you enjoy gaming, it is just fun)
Jojo's Bizarre Adventure
Paprika
Space Pirate Captain Harlock
Tokyo Godfathers
Wolf's Rain
Kino's Journey

Anime pretty much covers all genres. Some shows are better than others. No matter what anyone recommends look them up, read the synopsis and look into reviews. Because anime is more subjective, more than other mediums. This goes for any recommendation, EXCEPT for Cowboy Bebop, which is a masterpiece. Like seriously, if you watch one series of all I have mentioned you should make it that one.