I seem to be in a slightly different position to most of the people commenting here in as much as my copy is a boxed retail version allowing installation on unlimited PC's for home use. As such, I currently have it on two desktops and two laptops, all of which have been able to automatically update to the latest version whenever it's released for no extra charge. I bought mine on February 20th 2015. There was zero mention on the sealed box or the sale details of any further subscriptions ever being required . I have both the original box and the sale invoice in front of me as I'm writing this.
The only hiccup I've come across in the past three years is when I need to do a fresh installation, for example when I have built myself a new PC. If I download the latest professional trial version and try to upgrade it using my key it says it's expired, so up to now, I've always got around the problem by installing from the original disc and then upgrading to the latest version from that.That has always worked without a hitch. Today is the first time that hasn't worked and that's because I just bought a new tablet for my wife, which obviously hasn't got an optical drive so I copied the files from my original disc to a USB stick and tried to install it from that but got a system message that it isn't compatible with the version of Windows the tablet is running (It's the very latest Windows 10 October update one installed this week) So, I downloaded the professional trial version, tried entering my key, which of course didn't work and then came to this site to try and find how to fix it. I tried the "Lost key" link but that didn't work. I didn't buy it directly from Piriform so they don't appear to have any record of my email address. Finally I've come to the forum to see if it's known problem and found it is.
I haven't had any of these nag screens other people have mentioned. I was using the free version previously but paid $33.99 on the basis that it was a one off payment, was useful for my main PC to have the extra utilities it offers and the fact I could use it on my other machines was a bonus. They don't get much use so the free version is probably good enough for them anyway. There's no way I would ever pay an annual subscription for any software though. There are multitudes of programs offered free or for a one off payment as an alternative. I won't be happy if I get asked for extra payment to continue using what I already have, although I accept the time might come when Windows or PC specification progress might mean a completely different version might have to be purchased. I have a number of programs I've been using since the 1990's that I have had to replace with a newer version multiple times. However, I won't be considering anything that requires a subscription.
Although I bought the software from a US retailer, I am in the UK. In this country, and I believe, throughout the EU, it would be completely illegal to sell sealed software in a box that has no mention of a subscription and then request further payment a year later. That is classed as misleading advertising and can result in a court conviction and a large fine. In the case of multiple cases of such malpractice, the fines can run into millions of pounds or Euros as some of the biggest US companies have found to their cost. It is a grey area in my case though as the seller is in the States and I'm in this country so I'm not sure which consumer protection laws apply.
Anyway TL;DR, CCleaner Pro has definitely been sold in the past with the appearance to all intents and purposes of being subscription free.