The most common living room shelf setups I build for:
Above the sofa. This is the most popular placement. A single long shelf (48" to 58") or a pair of stacked shelves centered above the couch creates an anchor for the wall without competing with the furniture. I recommend keeping the bottom shelf 18" to 24" above the top of the sofa backrest so nothing gets bumped when you lean back. Depth of 8" to 10" works best here since you want display items, not deep storage, in this spot.
Around the TV. Floating shelves flanking a mounted TV replace bulky entertainment centers while giving you space for speakers, streaming boxes, controllers, and decor. Stagger the shelves at different heights on either side for a less rigid look, or line them up symmetrically for a cleaner feel. For heavier equipment like soundbars or game consoles, 10" to 12" deep at 150 pounds per stud handles the weight easily.
Flanking a fireplace. Shelves on either side of a fireplace mantel create balance and fill wall space that often goes unused. This is a great spot for stacked books, candles, and family photos. If you're also looking for a mantel, I build those in walnut and white oak.
Gallery wall alternative. Instead of hanging 15 individual frames (and putting 30 holes in the wall), run two or three floating shelves and lean framed photos and prints against the wall on each one. This lets you swap out art and rearrange without re-drilling. A picture ledge setup works best at 8" deep.
Filling an awkward wall. That narrow space between a doorway and a corner, or the empty wall at the end of a hallway leading to the living room. A shorter shelf (24" to 36") turns dead space into a display area without overwhelming it.
For more placement ideas, check out designing a perfect space with floating shelves.