I remember this thread being done too, but have no idea what it was named... The search function really ought to be made better I think!
Anyway.... Um.... It really does depend I suppose.
I have loads of sex toys and I have just split up with a partner. I am keeping all of 'my' toys, ones I bought for me. And that is almost all of them. I always used them solo, so they are 'mine' and not tainted by a partner. But I also have a couple of masturbator sleeves that I bought to use on him, and one of them that hasn't even been used yet, but I have just left them in my old bedside drawer and I suppose he will find them one day and he can do what he likes with them.
I think the general rule for me would be that anything that had actually been used on my previous partner would likely be ditched or left behind. Things like masturbator sleeves or anal tools or other toys that had been 'used'.
Things like vibes and dildos that are mine, are mine. If there are toys that I had used on myself with the previous partner in the bedroom etc then I think I would be fine with that - unless it was one or two specific toys that we used all the time together, then I would think about it.
Gifts would be different. As I said, I bought my partner at the time a masturbator sleeve that has never even been opened yet, but it doesn't change the fact that I bought it for him. I couldn't take that and use it with another partner in the future. Same if he had bought me any sex toys as gifts. They would always be from him and I doubt I'd feel comfortable keeping that. (Unless it was something superb like a Happy Rabbit! Then I would just have to keep it, probably!!)
That is just my mini-guide. But bondage stuff is a different world indeed! Some bondage stuff can be pretty expensive and I'm not sure what I would do if I had bought loads of bondage stuff and if we had used them together. (I do have a few bondage bits, but my partner was never interested in that.) I'd have no problem with using the bondage stuff I have currently as they were never used by us together, but if we had used them, then I think that some of it might have been a bit too heavily tainted by memories etc to be able to use with someone else again.
As for the stuff you do keep and (re-)use with another partner... well... It really would be down to your intuition on what you tell your new partner about the history of the sex toy collection! Basically, I would not keep anything that I would feel 'weird' about, as it will always feel quite awkward. As long as you have no hang-ups on what you have and what you introduce with a new partner, then your new partner should not feel uncomfortable either. I wouldn't produce a 10inch dildo and say "Ahh, I remember when *insert ex partners name* shagged me sensless with this thing!"
I would simply keep 'my' toys as 'my' toys and anything that I can't comfortably claim to be 'mine' would then be ditched or recycled through the amnesty on here (and get Oh! Points for new toys!)