Yes, common terms can be trademarked, but only when they are used in a context unrelated to their ordinary meaning.
A generic term for the goods or services it is directly applied to cannot be registered; "Bakery" for a bakery, or "Cloud" for a cloud storage service, would both be refused as descriptive. But the same word used in an unrelated context can be highly distinctive: "Apple" for computers has no descriptive relationship to electronics, which is precisely why it functions as a strong trademark.
The principle is that the mark must distinguish the commercial source of the goods or services rather than merely describe them. A common word used arbitrarily in a new context can do that; a common word used to describe the product it is applied to cannot.