How many different styles have you taking? (Open). Which and how long?

Lots.

Started with Seikukan Shorinji-Ryu karate from 1985-1999. Reached Shodan. Still run through the syllabus now and then.

Studied shoot wrestling intermittently from 2000-2003.

Been focusing on Mark Hatmaker's ESP system, based on Western boxing and wrestling, since about 2005. Certified coach.

Spent three years at Atlanta Martial Arts Center. My focus was BJJ, Muay Thai, and JKD. Also learned some Judo, Wing Chun, CSW, Keysi Fighting Method, and Inosanto's Kali-Silat from there, too.

Spent six months studying Goju-Ryu karate.

From seminars and cross-training, I've picked up bits of Five Animals Kung Fu, WTF TKD, Hapkido, Combat Hapkido, American kickboxing, Aikido, Panantukan, classic Jujitsu, Folkstyle wrestling, Shaolin Kung Fu, Kajukenbo, military combatives, and more.

I'm a martial mutt, but mostly it's Mark's system with some striking techniques from my karate days and some BJJ that come out in sparring.

Studied Motobu ha Shito Ryu Karatedo, Shorinji Toraken Ryu Kenpo and Jujutsu, and Mugai Ryu Meishi ha for the past 5 years under the same teacher.
Took Taichi, Xingyiquan, and Baquazhang for about 6 months.
Study Judo now since about April.

i lost count, seriously, when i was younger i use to spend a few months to a year in this style or that one, that i lost track.
i usually only count the ones i took for more then 2 year now as days, i took several styles of jujutsu, 6 iaido styles, 3 kenjutsu syles and 3 kobudo style, i only teach one iaido style and one kobudo style as well as shotokan, shito ryu and shindo muso ryu jojutsu

my short answer is
Shotokan karate for over 30 years
Shito-ryu for over 15 years
kobudo 30 years
iaido, iaijutsu, jojutsu and kenjutsu over 25 years
a couple of years of the following jujutsu, aikido, tai chi, goju ryu.