How often does GOG release a free game for a limited time and then withdraw the offer? For example if I didnt log into my GOG account for 3 months how many free offers should I expect to miss?

They'll usually tag a freebie to their major sales. There may be more than one, depending on how they structure it. Then there were some exceptional cases, like the Fallouts or the AvP beta test. So, for the last three months you'd have missed... 4 games and a movie? I think?

How often? Once in a while.
How many you are likely to miss not logging in for 3 months in a row? From 0 to a couple, no pattern. Then again, it depends on what months we are talking about. You don't want to miss December-Febriary, trust me.
Also you might have a look at this: http://www.gog.com/mix/free_games_temporarily_free_games ^Yeah, this too. Little Big Adventure, Mount&Blade, The Witcher 2, Age of Wonders, right? (And The Gamers: Director's Cut)

I still have keys for The Witcher 2 and The Gamers (Movie). Just let me know if you need them.

pretty much they gave away much more during the summer sale ( about 4 games )

wahaaaat I missed all those? They're all so awesome though, ive been robbed!

Just visit more often and you won't miss such great stuff again.

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+1. Or you could just, you know, actually buy some stuff.

Why would you go that long without signing up? I mean for a start we have a great community here, secondly the low prices are generally quite excellent so abusing GOG for freebies is not required.

Oh. Do you remember what those were? Besides Magrunner, I remember this one.

uhhh alan wake
the witcher ( off course )
and omerta city of gangsters

im very sure about alan wake and omerta not too sure about the witcher now thats just plain crazy

Magrunner, Omerta, Torchlight, Still Life and Alan Wake's American Nightmare.

Torchlight, Omerta, Still Life 2, Alan Wake American Nightmare, and Magrunner, I think. 5 games. This year has been crazy for GOG giveaways.

Honestly, the deluge of giveaways started last year during the Insomnia Sale. GOG offered a lot of different games for free in the midst of all that madness. Although, they were very small quantities available and they went fast. I really appreciate GOG holding this many giveaways. If I don't have a copy woo, free game! If I do have a copy, woo free game to give to someone else! It definitely encourages a positive vibe for the site and scads of customer goodwill. And it reminds people who may not live on GOG that GOG exists and they should buy stuff. :P

TLDR; Rock on, GOG!