The 55mm is razor sharp. I've heard professional photographers claim it's one of the sharpest lenses they've ever used. Amusingly, it was the first lens I ever owned for an interchangeable lens camera, so I didn't really appreciate it until I started trying other lenses.
The 24-240mm is very versatile, of course, but you pay for it in terms of both poorer image quality and substantial bulk. For travel, though, it has no equal if you don't want to carry extra lenses and keep swapping them.
The only other lens I've had is the 28mm, for astrophotography. It's reasonably priced, takes very good pictures, and it's quite fast (f/2).
Lenses I didn't buy but which I've heard great things about:
- 90mm Macro: if you're into macro, the image quality is supposed to be spectacular
- Zeiss Batis 85mm and 25mm: Not released quite yet, but early reports are very good
- 70-200mm: less versatile and more expensive than the 24-240mm, but faster and much better image quality
- 35mm f/1.4: Supposed to be an extremely good lens, but getting pretty pricey
Really, though, it depends on your type of photography. Landscapes, you'll want something pretty wide (16mm to 24mm), macro you'll want true macro capability, and wildlife you'll want as long as possible.