mine was when i was 18. a GTE visa with a 300 limit i only got cuz i was going to the national democratic convention in LA with my mom. i thought i was rollin' with my 300 limit!!!!. i listened to my mom and paid before the due date and paid more than the minimum and within 9 months, went from 300 to 1200. then, i went to college and screwed that up and many years later its now a 3000 (paid) judgment on my reports. 
I applied for a Citibank MC on college campus back in 1998 for some free stuff (t-shirt or candy bar), and they gave me a credit limit of $500-800 which eventually became 2100. I had no real job - maybe pulled in $20-50 a week. My interest rate was around 6.75% so I kept a balance while I kept paying down all my cards, and in 2009, they pulled the "we'll raise your rate to 19-22% (don't remember specifically) unless you opt out and let the account close" so I sadly let it close. I get credit card offers from them weekly, it seems. I liked Citi until they pulled the rate hike, so I'm not sure whether or not I'll do business with them in the future.
Starting Score: 557 (2005)
My first CC was through my CU (School's First Federal Credit Union), and I got it in 2005. My starting limit was $2,500, and it is now $3,900. I've only received one CLI from them over the years because they always do a hard inquiry for the request, so I tend not to ask for them. Interestingly though, when I did get the first CLI, they created a separate TL on my credit reports for the new CL of $3,900. I never disputed this, and I am glad I didn't because both TLs are still showing as open on my CRs and the opening dates are both from 2005. Furthermore, at one point I converted this CC to the "Gold" version and a third TL for this same card was placed on my CRs, again dated back to 2005. It makes me wonder if I ask for another CLI if they'll put a fourth TL for this CC on my reports with the new limit. My AAoA is only 3 years so this might help quite a bit, even with the hard inquiry.
1966 - BankAmeriCard - $500 limit.
I was drafted shortly after receiving the card. I used to wonder if applying for credit somehow put me on their radar . . . . 
My first CC was BoA secured visa student card wtih a CL of $300. This was opened in Sep 2006. At present it has been upgraded to Visa Signature with a CL of $5000.
@Itsmeagain wrote:1966 - BankAmeriCard - $500 limit.
I was drafted shortly after receiving the card. I used to wonder if applying for credit somehow put me on their radar . . . .
Im young again LOL thank you very much....
1988, a USAA MC or VISA (can't remember which, but it was one of the two.) $2,500 limit. That was a lot of money back then, no?
And I don't remember applying for it. In fact, I'm sure I didn't - they just sent it to me. Did they do that back then? I had just graduated from college - this must have been the trigger. To be honest, I didn't really understand what a credit card was. I knew it was something good, but I thought, "What does the $2,500 represent?" 
my first card was a Macy's store card with a 100$ limit... Still have it!