I imagine they could have some use, but I never bother. Partly because I hate using items in battles at all, and only ever use pokemon moves to boost stats. I just prefer to fight by my pokemon's actual ability than with bag items. Also partly because more often than not they just seem like a waste of time. Fortunately, they serve another purpose: selling.
In the games I think I would keep one of each for sorting purposes, just so selling them would be easier. The items do perhaps have a lot of development potential (think an "X-Sword" item or a "2x X-Attack" ability or hold item), and they are perhaps even quite exploitable (these are priority stat increases it should be reminded, this can help the Defense stats particularly and Psych Up in double and triple battles as well), but the games are simply too easy to win without them. If the games were less easy (not even being especially hard per se), then the items would maybe be remembered, maybe even used.
Never used those. Not only are there Pokemon moves that can be twice of four times as effective, there are now O-Powers, which have the same effects and don't even waste a move. As far as I can tell, they usually give me a free move while fighting Scientist-class trainers, and have occasionally won a fight for me in a close battle.
I'd probably use them if they could be used as a held item in like the battle spot or something. You send out your pokemon and the X-stat item activates. This would probably be too op, though. Like if first turn you send out Salamence with X-speed you get a ko, moxie prompts, it's unstoppable. You don't even have to waste time with a dragon dance.
The conclusion is, X-stat items suck and most likely always will.
I do, but not often. I'd rather try to get the battle done without the risk of getting hit. They're still useful, but again, I want to go for the kill. I might try to use them a little more often in the future though. I've seen some battles where I lost pokemon but could've won had I used one of those X items.
I've only used them a few times and that's just been out of curiosity. They seem pretty useless when compared to stat-enhancing moves, and don't even sell for much. I'm actually surprised they're still around, now that I think about it.