Question: Some time ago I've found a good online map for Alpine hiking trails. It was very similar to Google Maps and had green background.

I forgot the address and can't find it in google now. It wasn't myalps.net

Do you know this, or similar maps?

EDIT
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I've found this map in bookmarks on my old computer:

<http://alpenkarte.eu/>

Nevertheless the maps recommended in answers are very useful too. Thanks!

P.S.: I've been searching google 2 hours and couldn't find ANY of them. It seems like google isn't very good at indexing map websites other that their own...

Answer: 
The answers so far are already good, but I'd like to add a map for Switzerland:

<https://map.geo.admin.ch>

It's without doubt the best online map I've ever seen. It's amazing how detailed it is, and what kind of information you can shown on the map on demand, e.g. geomagnetic fields, employment density, or 4G antenna locations, but also more useful things for hiking, such as slopes over 30°, ski and hiking routes, borreliose risk regions, or ibex populations.

There are also tools available for planning, such as measurement tools, or elevation profiles, and obviously you can also expert and import GPS tracks. All this is totally for free!
Best Austria Alps maps are Kompass: 
<http://www.kompass.de/touren-und-regionen/touren/>

Switch layer to Summer/Winter in top right to see the details like marked trails and contours (otherwise it shows Open Street Map with less details). There are even winter ski tours there.