Assuming you mean the common green or green-and-white-leaved houseplant, then there's no reason to cut the stems off the plant unless you don't want little plants hanging down several feet from the mother plant. Leaving the stems on won't harm the plant in any way. Here's a plant that is horribly root bound (and will be until I repot it in March or April). It's in its winter quarters in my basement

As you can see, it has more than a few babies.It's also blooming.
UPDATE
Thanks for the excellent photos! They show the offsets forming from the mother plant, before they start drooping. In fact, the first photo actually shows the flower buds while the second seems to show a stem that's beginning to branch. Don't cut these and your plant will flower along the stems, with the plantlets forming a little later. Because your plant is trying to flower, I recommend leaving these stems because cutting them will actually weaken the plant—it will keep growing offsets to replace the ones you cut off. If you don't want the plantlets, then cut the stems after the flowers fade.