What focal length lens is your favorite for your camera – digital SLR?

Fix-Length Lenses Are Best.
I like any fixed lens for four reasons.
(1) In general, fixed (a.k.a. prime) lenses have much simpler optics than zoom lenses. That means that images are generally sharper, with better contrast and fewer aberrations.
(2) Simpler optics also means that the apertures can be wider, letting in more light through the viewfinder in digital SLRs. A typical zoom lens can go to f/4.5 to f/5.6. Fixed lenses typically go to f/2.8 to f/1.4, letting in four times as much light. That makes seeing through the viewfinder much easier.
(3) Because larger apertures are possible, depths of field can be made very shallow. That is, backgrounds become much more blurred, often beautifully.
(4) Because optics are simpler, using fewer pieces of glass, lenses are small and lighter.
24mm & 50mm lenses
(for full 35-mm sensor cameras)
18mm & 35mm lenses
(for digital SLRs)
I like the 24mm lens when I want a wide angle lens that does not produce much distortion. I like the 50mm lens when I want tighter crops, or when I want to be further away from the subject. Again, cameras with digital sensors need 18mm and 35mm lenses to get the same photo as 24mm and 50mm lenses on full 35mm sensors.
If you want to do close-ups, get a macro-lens, a lens made to focus up close.
There are zoom lenses with good optics, but they are very expensive, usually a few thousand dollars each. They are often heavy, but they can have apertures of f/2.8.