Bicycle Mechanics - wheel slips forward in horizontal dropouts

Both of my road bikes have horizontal dropouts, and I have trouble with the drive side slipping forward in the dropouts. I'm not mashing the pedals particularly hard or trying to start out in the tallest gear. I have standard 130 mm hubs in frames with 130 spacing. The only solution I have found is to tighten the skewers really hard, but I have actually broken a couple of skewers this way. Any ideas?

Once you tear the wheel forward a few times, it may begin ripping up the metal on the inner face of the dropout, so that it won't hold well in the future. Been there, done that. I resorted to having a framebuilder pal replace the horizontal dropouts with vertical dropouts. Problem solved.

Other than that, make sure your hubs' driveside locknuts have nice sharp serrations. At this point I'd bet they're chewed up too, so you may want to go to a good shop, explain the problem, and ask for some gnarly new locknuts.

What kind of quick releases?

Most of the aftermarket quick releases have a visible, external cam. Quick releases that have their mechanism hidden, like Shimano, grab a lot more tightly.

Both of my road bikes have horizontal dropouts, and I have trouble with the drive side slipping forward in the dropouts. I'm not mashing the pedals particularly hard or trying to start out in the tallest gear. I have standard 130 mm hubs in frames with 130 spacing. The only solution I have found is to tighten the skewers really hard, but I have actually broken a couple of skewers this way. Any ideas?

It's possible that you have too much of the axle exposed on the drive side. With a QR, the end of the axle must not protrude past, or be flush with, the outside face of the dropout. It should be at least 1mm short of being flush with the outside of the dropout, or you will experience exactly what you describe - the right side of the wheel will pull forward when you pedal. No amount of tightenning the QR will fix this problem. If the axle is too long on the drive side you can either cut down with a hack saw or dremel tool, grind it down with a grinder, or re-center the rear axle by shifting everything (locknuts, cones, spacers) towards the right side. You can't have the QR axle too long on the non-drive side either. If you dropouts are, for example, 5mm thick and your hub is a 130mm O.L.D. then your axle should be a couple of millimeters short of the (O.L.D. + combined thickness of the dropouts) dimension. So, in my example that dimension would be a couple of mm short of 140mm. This is why one of the standard lengths for a replacement axle is 137mm. That axle would be 1.5mm short of flush with the outsides of the dropouts on both sides of the bike.

This may not, in fact, be your problem, but it is such a common problem that it's worth a look. This happens frequently when people service their rear hub and take the rear axle, and it's components, completely apart. You could lengthen the right end (past the locknut) by as little as 1mm and cause this problem. For this reason, it's a good idea not to unlock the locknut on the drive side when you overhaul the rear hub unless you have to. If you do, just make sure that the end of the axle protruding past the locknut is 1-2mm less than the thickness of the dropout.