It's a nice feature, but not primary. If I'm gonna buy a new hardware is for new games, right?

I do. That's why I don't want to leave my Wii just yet... I don't want to lose GC compatibility.

It defines how fast do I buy the next gen, I usually have a backlog and if I cannot play it on the new console, I can wait to buy it till a later date. Right now I plan to buy a PS4 or Xbox One on holiday 2015, but I just bought a Wii U last week.

It's convenient to have, in cases that if my Wii stopped reading disks or just dies, I could just play them on my Wii U

If your console has it and others don't, you care!  But if your console doesn't have bc then you use words like "honestly" to describe your lack of caring.

On PC BC is very important, and the issue is also more complex: while PC gaming has a lot of nice features, BC is becoming the only reason to keep doing PC gaming with Windows. Weren't for BC and its huge legacy, it would be better to drop that bloated and closed Windows and switch to a lightweight free OS, like SteamOS or other specialized Linux distros or Android. The situation could change if most new PC games will start having a Linux or Android version too, because on PC (and recently on consoles too), as a legacy game becomes older, its emulation becomes easier, this because its compatible SW-HW platform and its minimum and recommended HW requirements are frozen to the time of its release, so its acceptable emulation is just matter of time, to refine the emulator and to have enough HW power to run the emulation at the same speed or even better than on the original SW-HW platform.

Yeah, its. A major thing for me. Why? Because new consoles don't have the best lineup of games and suffer from dry patches. Instead of not turning on the system, I get old games I never got round to and play them on my shiny new system.

No BC means no sale for me until a library is built. And asking general people who are vaguely interested, it seems to be a similar approach for them. Why pay £350 for a system when you can't play your library of games on it?

I'd say having the ability to transfer your eshop games over to the new system is a very big deal. I would be upset if I owned a PS3 or 360 and couldn't transfer those games over day 1. Sony will supposedly have a fix for this in future but I haven't heard anything since the deal with it or whatever comment by Microsoft.

Ability to play previous system games?  Use it more often on hand helds but I have used it a decent amount with Wii/GC and Wii/Wii U.  So it is a nice feature especially when you have a ton of good games from a previous system.

If ps3 would have stayed BC, i would have bought one much sooner than i did.
I would have loved to be able to play ps2 games on the one system that is in my living room. I couldn't so i didn't.

I did care back then, now i am used to not being able to play previous generation games. They even trapped me into buying HD remakes of those games.

Funny thing though, while complaining back in 08/09 about the disappearance of BC there were a lot of people very much okay with that disappearance and telling the 'pro-bc' guys to stuff it. Seems like some people changed opinion.

For not having BC my purchase of a next gen console will be postponed by several years.

I used to care, but not anymore. I emulate my PS1 and PS2 games on my PC now.