I think it depends on a lot of things.
Maturity of the person, maturity of the prospective person to be dated, planned activities on the date, etc.
I was allowed to "date" at age 13, but there were odd factors at play. My parents gave me a lot of trust (I was a good kid, especially compared to my sister). The girl I was dating was also very mature and trustworthy (we knew each other through church, and later through her school's dances.) It ended well. Typical grade-8 wholesome fun. When I was a teen, I almost never dated at all. Half because all the girls I knew lived several towns over (I went to school outside my town) so it was really inconvenient, but also because I was really bloody shy back then. I was also socially awkward. When I liked a girl, it SHOWED. I must've been just one or two steps removed from the guys in The Creep video. Got better in University (you get more mature from being so far away from home), and got better still when I stopped obsessing about trying to get laid. Met a nice girl in the summer after third year, married her in July 2010.
Now, if I had a child who was not very mature, who I could expect to get into a lot of trouble, then I wouldn't let him/her date until they were older.
I think it's different with girls too (daughters, that is to say). Because you don't just take into account the maturity of your daughter, but also the maturity of those she wants to date. And I remember how my brain worked (or didn't work) when I was a teen. I remember showing outward maturity while secretly coveting sex. I know what teenage boys want, and I would protect my daughter from that. I know it's a double-standard, but I feel it's a fair one. Fathers are almost hardwired to turn their sons into Men, but protect their daughters at all costs.
When I have a daughter, I will purchase many weapons, and prominently display them in my office (I'm thinking a sword, some shurikens...you know, things you buy at Comic Con), and have a chat with any of her prospective boyfriends in front of all the weapons. Use phrases like "I'm ok going back to prison" or "If you come home after curfew, your engine and headlines might make me flash back to the helicopters flying over <insert war location; I'm thinking Hanoi or Kandahar or wherever>".
-Sparks Nevada, Marshal on Mars
"Who cares what evil lurks in the hearts of men!"
"Unless evil's carrying the Martini tray, darling."
-Frank and Sadie Doyle