My dad was a chemistry professor. He used to say that he could have done any job, but the idea of being a "scientist" really excited him when he was young. From an early age, I think I kind of held on to the idea that you don't change who you are based on the title of a job. You can do any job, but you are still you.
I worked as a programmer all through school (working for computer services at the university, or for various labs). When I graduated, I ended up travelling a bit and worked doing odd jobs at a travel tour company in London. If you've ever seen the movie "The Secret of My Success" with Michael J Fox, then this is pretty much what happened to me.
I got stuck in the mail room one day and was appalled at the ridiculous process they had. When a fax (or more commonly in those days, teletype) came in, you had to route it to the director of the department. That person read the message and sent it back to the mail room. Then you sent it to the manager of the department. That person read it and sent it back to the mail room. After about 3-4 rounds of that, it would get to the person who actually needed to read it. One day we got a message from a hotel that there was a problem and that they couldn't accommodate the bus that was coming in -- in 3 hours. So I photocopied the teletype, sent the original to the director and the copy to the person who could actually solve the problem. Later the managing director came down from on high (literally) and thanked me for helping. It became my job to read all the incoming mail and make sure that the appropriate person got mail as soon as possible.
You should have seen the backlash in the company. People were incensed that this young kid was reading all of the mail and was making decisions about how to route important information. Someone even told me, "I've been working here 10 years and I've never even seen the MD." -- and not in a friendly way. But after that point the MD loved me and there was nothing they could do.
Another day, they asked me to wander up to the finance department to help with year end filing. Usually it took them 2 weeks to file all of the tax related papers for the year (because everyone was too lazy to file them as they came in :-P). Of course, I'd just spent 4 years learning every stupid algorithm on earth (the disadvantage of going to a school with a crap CS program) and I knew sorting :-). So I sorted the files. I took over a whole room and started putting papers in seemingly random order. People came up and asked, "Why are you doing it like that?" and I replied, "I don't know -- that's just the way you do it". It was sorted in 2 hours. The finance team thought I was a freaking genius and soon I found myself moved up from the basement to the fourth floor (2 from the top!). I refused to wear a suit, but the MD loved me anyway (and mostly everyone else hated me).
So I was working in finance and also reading everybody's mail when I noticed that the computer department (such as it was) was having very interesting conversations over internal mail. Long story short, they were embezzling money and essentially forming a plan to hold the company hostage so that they could spin off a separate company to perform services for them.
So I sat down and started writing up a plan to replace their ridiculous system with something that would actually work (and include a system to email faxes and teletypes to people... I mean, come on). Just basically doodling around with it in my spare time. Eventually I had the plan ready and was about to talk to the MD when...
I decided that I'd had enough of business :-) I went back to Canada and farted around in school for another year. Never did give the MD my report or tell anybody about the computer division's plot. The company is still in business something like 30 years later (and I think doing fairly well), so I guess it was fine. But the key is that it just didn't matter what my "job" was.
As you say, "Over time opportunities will pop up". Maybe in not such a ridiculous fashion as my experience, but they do. I've worked as a programmer for decades, but I also once quit my job, moved to Japan and taught English in a high school for 5 years. That job was also fun. There are hidden depths to anything you can do. Just keep in mind that there are some organisations and people who will just treat you like crap all the time, so avoid them. Other than that, you're as free as you want to be.
My favourite quote from Dr. Who was when someone asked who he was working for and he replied, "Work for? I don't work for anyone. I'm just having fun." I try to treat all of my jobs like that. I suppose I technically work for someone, but my attitude is that if I occupy myself with interesting things that benefit my boss, then nobody (important) will complain.