There is A LOT of misinformation about nenkin. Few people understand the system well.
And since I am weird and know quite a bit about it, here is everything important about nenkin and all the supplementary systems available.
Everyone living in Japan between the ages of 20 and 60 must register for and pay into nenkin.
If your income is low enough you may qualify for a partial or full exemption. If you get an exemption you will still get credit towards your pension (at a reduced rate).
If you are employed and working full-time, your employer will generally enrol you in shakai hoken, which includes kosei nenkin and health insurance. You will pay part of the contributions, and your employer will pay the other half. Payments are based on your income.
If you are a freelancer, self-employed, or your employer won't enrol you in shakai hoken you should join kokumin nenkin. Kokumin nenkin is a fixed monthly payment (currently 16,590 yen).
Contributions to nenkin are tax deductible (both kosei, kokumin, and the supplementary schemes described below).
iDeCo is a self-managed investment account. You can pay in between 12,000 and 68,000 yen a month (depending on what kind of nenkin you pay) and decide what to invest it in. The contribution is tax deductible and you can't access the money until you are 60.
Fuka nenkin is a scheme for kokumin nenkin payers. You pay 400 yen extra a month and get a slightly larger pension. Very good rate of return on a very small amount of money. Uses the same tax allowance as iDeCo.
Kokumin nenkin kikin is a way for kokumin nenkin payers to 'buy' extra pension. It uses the same tax allowance as iDeCo. For most people iDeCo will be better, but this might be good for people who don't trust the stock market or US citizens (who can't use iDeCo).
After 120 months (10 years) of contributions, you become eligible to receive a pension from Japan from age 65 (you can claim a smaller pension from 60, or defer up to 75 to get a larger one).
People claim nenkin will go bust or not pay out in the future, but I think that is unlikely. The Japanese pension fund is one of the largest in the world, and I can't imagine any government defaulting on their pension obligations.
Nenkin payments are increasingly being considered for visa applications, and I can only imagine this will increase in the future as My Number functionality is increased.
If you leave Japan you can get a refund of up to 5 years of nenkin contributions.
Not having a pension in old age is a very bad idea, so if you live and work in Japan check out your nenkin options and make sure you are preparing for a comfortable retirement.
You will need more than nenkin, of course, so you might also check out tsumitate NISA or taxable investment accounts. Come to retirejapan.com for more information and ask questions in our forum!