Photo manager that organises by folder structure

digiKam (Click to Install)

digiKam is an image organizer and editor using KDE Platform. It runs on most known desktop environments and window managers if needed libraries are installed. It supports all major image file formats, and can organize collections of photographs in directory-based albums, or dynamic albums by date, timeline, or by tags. Users can also add captions and ratings to their images, search through them and save searches for later use.

If you are using GNOME here's how to make digiKam look native .

Darktable

In answers to this question you will find a good selection of photo managing software in addition to F-Spot. Amongst those suggested I found Darktable to not only look good but also have many useful features when it comes to organize your collection:

This project is in active development. More recent version can be installed from the official PPA ppa:pmjdebruijn/darktable-release .