I take them all... in the future when I retire I will have time to play them all (or at least try them). In my backlog I only put games that I buy with my own money or that I wanted to buy but I got for free and games that I got from giveaway from forum user here on gog.
That way my backlog got smaller but I still got a lot of games in my library that I can decide to play in the future (and I will not need a stupid gamepass).

You must be fun at parties.

I have not taken one single free video game yet.

No, because I learned better to pick games I'm interested in over useless clutter.

Most of the time, I've already bought whatever is being given away.

On GOG, I take them all because they're either classics or otherwise look neat. On Games With Gold on Xbox however, I'm more picky. If it's anime fighting games or games that have low ratings, I skip them. Some of them look like straight trash.

Quality freebies like those that frequently appear on GOG and Epic I almost always take even if it'll never make it on my play list. Low tier freebies I usually avoid unless it has a special appeal to me and I'm sure to play it.

I take all of GoG's freebies because even if I don't play the game given, someone else might want to and I'll have it available for them.

However, i don't participate in giveaways with a limited amount of games i have no interest in playing because I don't want to take away someone else's chance.

Not always. I usually do take them unless they don't really appeal to me (for example, I don't usually enjoy horror or FPS so I think twice before redeeming them).

No. I take it if it's a thing I acually wish to have. Not hoarding things (even virtually, but what does it mean given it takes room on physical support) just because i can it's free grabby grabby gimme gimme.

We live in a world of maximising gain and accumulation no matter the reason or lack of, no matter how absurdly, but just because it's, by mere principle, the thing to maximise. Just because it's our cardinal value, by itself, without any specific object. Like it's its own reward. I find this encouraged mindset tiresome and slightly sickening.

If it's easy to get them (e.g. I already have an account and just need to click a button), they are more or less quality games, and there is no disadvantage in installing them (e.g. third party account required or aditional DRM), then I do, most of the times, even when they're not in my preferred genres and I'm not all that excited about them. Just in case, to give them a try some time, when I'm bored. Not "always" though. Occasionally, if it's a game I'm a 100% sure I will never want to try or I even dislike the concept or the devs, I don't even want it in the "Probably not going to play" part of my collection. Or if it looks like shovelware, worse than any freeware game I could download, I don't bother either.

I am absolutely, categorically not interested in 90% or more of all games and absolutely, categorically never will be. Ever. So I skip pretty much 90% or more of all giveaways.

Even so, my Pile of Sha–Opportunity is big enough to last me a lifetime. There is absolutely no point in cluttering my library with stuff that ranks about the same on the things-I'd-like-try scale as ripping out my toenails with hot pincers...

On GOG, I take any time-limited freebie on offer, as long as it's not also both limited in quantity AND something I would be unlikely to enjoy -- and I don't remember there having been any limited-quantity, direct-claim freebies here for years.
However, for games that are either released here with a regular price of "free", or have the price changed to "free" later, I no longer redeem a copy unless I'm likely to play it soon (unless its availability is also time-limited, like that Christmas-themed Cave Story spinoff that Nicalis released a year ago).

On other platforms, I only redeem freebies that seem interesting (with a greater likelihood if the giveaway is time-limited), and only if it's either a DRM-free direct download from that site (i.e., no publisher or store client required), or a copy that's redeemable on another DRM-free-friendly service that I already use (the Humble and Amazon Prime giveaways of GOG copies of games being my only experiences with this).

I'm much less likely to just take the freebie and worry about [whether I'll ever play] it later on "open marketplace"-style stores like Steam (irrelevant for me) and itch.io than I am on more curated stores -- in part because, at least on itch, there are often hundreds of free games available at any given time, and a lot of them are: unfinished, prototypes, or otherwise not full games; games that are maybe decent enough, but just "not for me" (e.g., almost anything anime-inspired...and there's a lot of that); or just garbage (low-effort meme-based stuff, "this my firts ever game ok plz b nice", etc.).

I always take DRM-freebees.

I'm still developing my sense of what games I like and what I don't. Freebies have helped expand my horizons, so to speak, because my real spending is strictly confined to what I know I already like in games.

I've been pleasantly surprised with some freebies and it's opened my eyes to some genres/gametypes. Others have been immediate uninstalls. Strange though, but I've found some games either freebies or given as gifts to be more enjoyable than the games I've actually bought, which proves I'm not the best judge of what games are better suited to me!

So, like Timboli, I have a habit of claiming them all with the intention of eventually sampling them and having something there in the future which I may decide I might like to play.