I've been very unlucky with illuminated keyboards, with both last ones you had to look at 90 degree angle to see the keys and the monitor light itself made it very difficult to see.
Only in total darkness and at right angle could you actually easily see the keys.

Has anyone managed to produce a proper illuminated keyboard?

Logitech Illuminated, Logitech K800, Ducky Shine.

I've used these keyboards and know their backlighting to work very well, particularly the Ducky Shine, which could light up a room on maximum brightness.

Too bad it is ruined by being wireless so it needs charging, I don't want to think about charging basic stuff...

anything else?

Logitech Illuminated Ultrathin Keyboard with Backlighting, its a good option, it has low travel of the keys, but imo not that noisy and the illumination is good, and its wired so no recharging or worrying about batteries. Another decent is Deck Keyboards but this are mechanical so they will sound much more, but they will also last more and the actual feeling of typing is better, but this is very subjective to each.

This one looks best illuminated
(click on 01:10)

Any experiences?

I have two K800 keyboards (one at home and one at work) and they are the best keyboard I've ever used. Saying it is ruined because it is wireless makes no sense at all; the wireless is an OPTIONAL feature that you don't have to use if you don't want to. Just leave it plugged in all the time and --surprise!-- it will behave like a wired keyboard. I use it wireless, and honestly I charge it less than once a week; it is remarkably power efficient.

As an aside, it turns out I have very limited use for an illuminated desktop keyboard; they are extremely useful on laptops, just not so much on a desktop with a 24" bright glowing screen towering above it, or in an office surrounded by fluorescent light. Regardless of that, the K800 itself is an absolutely fantastic keyboard that is supremely comfortable to use for extended periods.

(disclaimer: I work for Logitech, but not on any product related to keyboards/mice)

So I have the K800, which is the "wireless" version of the Logitech illuminated keyboard linked above, and I love it. The weird thing about it is you can really use it wired or wireless--it charges via a supplied USB cable. Generally I leave it plugged in, although it seems to last quite some time unplugged (weeks?) with daily use.

The backlighting is spot on; it only turns on when your hands are near the keyboard. Also nice is the universal receiver (tiny USB dongle that works for both keyboard and mouse, and a bunch of other peripherals). One of the best keyboards I've ever personally owned. My only wish would be some sort of touchpad I could easily use with gestures.