I used quarter round in my bathroom for the same thing. The only time it bothered me was when I was lying in the tub and could see the tiny gap between the tile and the quarter round trim. Glass of wine and a good book and I'd forget all about it til next time. :-)

In a kitchen I've used that thin, flexible luan type stuff used under the toe kick to hide seams between the different cabinet boxes. I'm rarely, if ever, at toe kick height so it's never been an issue to bug me. 1/4 inch gap sounds like maybe a handmade or variable natural product like slate, so I wouldn't worry too much. Start with kick material (I'm sorry I can't remember the name, maybe kickplate? I'm diy not pro), you can always add quarter round or a different trim piece - our current house has almost reversed quarter round, instead of a hump like shoe molding and quarter round, it has a scooped profile, like a half C. If that's not enough, you could caulk the gap and paint to match cabinet.

This post was edited by MiaOKC on Wed, Aug 7, 13 at 20:07

Quarter round or shoe molding is typically used to cover those gaps. I prefer the shoe because it is less bulky and more refined looking.

I would think the toe kick piece would also be able to cover it if you don't want molding along the bottom of the cabinet.

P.S. And a good tile man would have made sure the floor was level and flat before putting the floor in ;) That's good prep and foresight.

This post was edited by snookums2 on Thu, Aug 8, 13 at 14:38

IMO, quarter round is the cheap and ugly.

Any 1/8" or 1/4" plywood / hardboard - ripped and stained / painted can be tacked right over the old toe kick.