Are potions of mutation useful?

From what I understand, mutations can be either positive or negative. Drinking a potion of mutation will give you a random mutation, so there's a good chance that it can ruin your game for you. Is it worth holding onto these potions? Is there a point in the game where drinking one is actually a good idea?

Also note, as the game changes over time, the answer changes. From the dev blog in feb 2017 (about the current Trunk and presumably the next release):

Potions of mutation, cure mutation, and beneficial mutation have been blended together into one big slurry! They (potions of mutation) now removes 2-6 mutations, adds 1-3 random mutations, and then adds another 1 ‘good’ mutation, which is essentially similar to drinking all three old potions in a row.

See https://github.com/crawl/crawl/commit/b9e5f3fc1c77b7484e45122498c1692b8fab371f for details and philosophy.

It really depends on how you want to play the game. Crawl players refer to drinking mutation potions as the mutation roulette. I quite enjoy playing the mutation roulette, but some prefer to play it safe. I would recommend dropping them as you get them, in order to keep them safe, and then once you have a potion of cure mutation, drink them one at a time and see what mutations you get.

After each one, you need to decide if you want to drink more, or if you want to cure your mutations. The first one isn't much of a gamble, because if it gives you bad mutations, you can just cure them away. The second one is more of a gamble, because if you get very bad mutations from it, you're going to want to cure them, which will also remove the good mutations from the first potion, as cure mutation removes 1-7 random mutations. I usually stop after two good potions, as I feel that the risk of losing all the good mutations outweighs the possible benefit of gaining a few more.

One last thing to keep in mind is that potions of gain strength/dexterity/intelligence are simply targeted mutations, and thus will be removed by cure mutation.