Is is well known fact that marine mammals and some birds can sleep with one brain hemisphere at a time, since it's essential for their survival.
However, at least in my opinion, such mechanism would give significant advantage to many other species (e.g. to antelops) because it helps avoiding predators.
While answers to this question explain why sleep is necessary, animals with unihemispheric sleep mode does not seem to suffer from any of mentioned drawbacks of non-sleeping (except maybe increased energy consumption).
Are there any particular disadvantages of unihemispheric sleep versus "normal" sleep?
EDIT: I've stumbled upon the following paper: Rattenborg N., Amlaner C., Lima S.. 2000. Behavioral, neurophysiological and evolutionary perspectives on unihemispheric sleep. Neuroscience & Biobehavioral Reviews 24: 817–842, which discusses several possible reasons for absense of unihemispheric sleep in most mammals, but does not present any evidence to support their hypothesis. The main reason (from authors' point of view, at least) is the need for very loose coupling of both hemispheres to allow them sleep independently, which might negatively affect overall brain effectiveness.
Along these lines, sleep may play a role in integrating the functions of different brain regions. Thus, BSWS1 in terrestrial mammals may be superior to the BSWS in animals with USWS2 because it allows integration within and between hemispheres, rather than just within a particular hemisphere.
Specifically, the reorganization of the central nervous system required for USWS may interfere with other adaptive brain functions, such as integrating the functions of both hemispheres.
1 Bihemispheric Slow Wave Sleep; 2 Unihemispheric Slow Wave Sleep
They also argue that the unihemispheric sleep might have been present in first mammals, but wasn't giving any advantages on first stages of evolution.
However, this paper was published more that 10 years ago, so there might have been some advances in the field since then.