How do I avoid carrot slices rolling away?

One thing I've done in the past is use the tendency to roll to my advantage, rather than fighting it.

I position a shallow dish to collect the carrots at the "bottom" of the cutting board (the edge furthest away from me), and prop the cutting board up slightly at the "top" end (where I stand). I use a kitchen towel, since that keeps things from sliding around. As I slice, the carrots that roll have a natural tendency to roll into the collection dish.

Another strategy: What I have been doing lately instead of propping up my cutting board on a kitchen towel, because I'm lazy, is to slice my carrots on a bias. They are still round slices, but they are slightly elliptical and don't roll as well.

If you take a slender slice off the carrot (down the length), then your carrot is no longer round, and it'll nicely sit on that now-flat side. (You can do this with a sharp knife, or with a few passes of the vegetable peeler). Visually, though, it's hardly noticeable especially after cooking.

Easy-peasy:

1. Use a mandoline: they'll fall mostly on their flat side
2. For the difficult ones that do not fall under the category mostly: place the mandoline over a bowl.

One option is to cut the carrots slightly diagonally instead of perfectly square. The resulting pieces are not perfectly cylindrical, but they tend to tipping instead of rolling all over the cutting board. (Note that this method only works if the diameter of the carrot is substantially larger than the thickness of a piece.)

I use a reasonably large cutting board with a "drain" around it (the kind that would also be suitable for cutting meat and has a medium-thickness notch cut around the entire perimeter of the board). That way, when the inevitable freeroller happens, it rolls into the drain and stops.

I recently discovered that if you put the carrot inside a stalk of celery and slice it, it doesn't roll around. Usually i add celery to whatever disk has carrots anyway

Rotate the carrot a quarter turn and again cut at an angle.
This will prevent the slices from rolling off the chopping board.

It may be because you have peeled them. Did you know the relative majority of nutrients is in the skin, it is the most important part of the carrot. When it comes down to it, you don't ever really have to peel carrots. The friction is greater with the skin still on they don't roll far. As long as you wash and scrub them well to remove dirt and any debris, unpeeled carrots are perfectly safe (and delicious) to eat. Here are five instances that prove it, stock, roasted, stewed, pureed, juiced. But of course cooking also destroys a lot of the goodness. I also have a cutting board guard to stop any strays. I like cinnammon with cooked carrots, but most of all I like them raw with peanut butter. I have left some out for the Easter bunny.

I agree with many of the suggestions above. However, if your carrots are still rolling off the cutting board, consider putting one or more rolled towels around the edge of the cutting board to prevent the "rollers" from escaping their inevitable fate.