I was single, but the programme
does accommodate families. I've even met more than one single parent on the programme (and universally it seemed to be a wonderful experience for the child, which surprised me greatly). The spouse even gets a working visa (or did 10 years ago when I was on the programme). It's a great job.
I haven't looked at the situation recently, but there used to be an age limit of 40. I applied when I was 38, which is essentially the very last time you can do it.
In case you (or anyone else) is interested, I'll write a few things about my impression of what the JET programme is (which differs slightly from the official version). The official version is that JET is the "Japan Exchange Teaching" programme -- so the idea is that people come to Japan to teach English. In reality, it is a rather brilliant plot by the Japanese government to both get rural people used to having foreigners in their communities, and to expand awareness of Japanese values abroad in order to soften the position of foreign powers in business and trade negotiations.
Basically, what was explained to me by a few Japanese government officials (after many, many beers) is that in the 1980's Japan was flying high in the world economy, but they were having a lot of trouble with the rest of the world understanding how they did business. There are some great English language documentaries on the subject (I wish I could remember some, but I suspect you can search on Youtube to find some good ones).
You would have American sales people coming to Japan and saying, "We make car parts. Our parts are 30% cheaper than your supplier. You should buy from us". And the response would be, "We've worked with our supplier for 250 years and have developed a level of trust with them. Why should we betray them for a mere 30% discount" Even small things like people showing up for discussions with important business people and not bringing a souvenir as a gift, or refusing to suspend conversations until everybody had properly gone out and had a drinking party would derail a lot of trade deals.
At the same time, the Japanese government was thinking, "Our population is getting older and if we keep growing financially we're going to have a massive labour shortage". But the vast majority of Japanese people had never seen a foreigner in their life. They realised that they needed some kind of cultural shift to accommodate the bringing in of foreign workers.
They concocted this really bizarre plan where they would seek out and hire young, educated foreigners who are from rich connected families and bring them to Japan for a few years. The idea was to indoctrinate these young people with Japanese ideals and then send them back to their home country. Then 20 years later, those young people would inherit their thrones (remember they are from rich, connected families) and they would be in a position to change foreign policy towards Japan. They would also be able to educate foreign businesses how to communicate to Japanese people. They would also send these young people only to rural locations (where there are no foreigners) to pave the cultural way for the inevitable influx of foreign workers.
I think we're getting up over 30 years of the JET programme and it has been a crazy success - from that perspective. There has been a problem, though. When they initially set up the programme, they didn't know what the young people would do. Someone had the bright idea of having them teach English at the schools. So that's what they did. However, young, rich, snotty-nosed kids right out of school... ummm... They aren't necessarily the best workers (of course there are many exceptions to prove the rule!). In fact, historically quite a large percentage of them had never had a job in their life. They didn't know how to work, had never had any real direction in their life and were also suffering badly from other kinds of culture shock. To top it all off, virtually none of the teachers in the school system wanted these people and took it to be a particularly onerous babysitting job.
Over time, the programme has started to hire a percentage of older people into the programme. They still look for people with good connections. Even though I do not come from a particularly wealthy family, I worked for some of the largest and most influential tech companies in the world. That's the kind of thing that has the JET programme licking their lips. You get a person with that kind of influence and a proven track record of working hard, it's great for them. They can send that person to one of the schools that are pissed off about the people who have worked there before. For example just before I came they had to fire a guy who never once showed up for work -- he went surfing every day. They needed somebody that would keep a low profile and just do what they were told.
The JET programme in Japan, despite being wildly successful in their unadvertised nefarious plan, is under a lot of criticism for their public role. The JET programme pays a lot more than private companies charge for "assistant language teachers". Quite a few schools have moved from JET assistants to assistants from private schools. The advantages are many: usually the workers are older, experienced in teaching EFL and they are a good %30 cheaper. Why should a school hire JET assistants?
This has caused JET to hire actual teachers! These are people who have no money and no connections and are probably not a good fit for the original goals of the programme, but they can actually do their job when they are in Japan. I think there is some hope that the teaching skills will rub off on some of the others (it doesn't, but it's a nice thought...).
So that's where it stood about 5-10 years ago when I was involved. I'm not sure how it's moved on from there. But basically they have 3 categories of people that they are looking for - 1. young, rich, connected people from famous universities; 2. older, connected people who have life experience; 3. people with qualifications in teaching. I think you're still more likely to get hired if you are in category 1, but there are a fair number of positions in the other categories.
Disclaimer: many tongue in cheek comments -- I apologise if anyone found it offensive rather than humorous.