One might think all we do is stamp-collecting.

• Mathematics
  • Classification of simple finite groups
  • Classification of manifolds and surfaces
    • Regular polytopes
    • Elementary cellular automata
    • Symmetry groups
      • Wallpaper groups
      • Space groups
      • Bieberbach groups
    • Classification of reversible bit operations
      • Also Post's lattice
    • Complexity classes and their relations
      • Arithmetic hierarchy
      • Polynomial hierarchy
      • Chomsky hierarchy
    • Stability theory
      • Poincaré maps of linear autonomous systems
    • Game theory
      • Classification of $2\times 2$ normal-form games
• Physics
  • Standard Model
    • Classifies all fundamental particles
  • Cosmology
    • Stellar classification
    • Galaxy classification
    • Orbital mechanics
      • Lagrange points
      • Different types of orbits
• Chemistry
  • Periodic Table of Elements
  • Synthetic polymers
  • Hazardous materials classification
• Biology
  • Phylogenetic tree of life
  • Linnean taxonomy
  • Classification of viruses, e.g. the ICTV classification
  • Various schemes for biomes, e.g. the Holdridge life zones
• Earth science
  • Geologic time scale
  • Cloud genera
  • Soil classification: USDA soil taxonomy
  • Classifications of snow and snowflakes
  • Classification of minerals, separated beautifully into:
    • Organic
    • Silicate
    • Non-silicate
  • Also meteorites
  • Trewartha and Köppen climate classifications
• Linguistics
  • International phonetic alphabet
  • Language families, list
  • Unicode
• Medicine
  • Medical classification: ICD-10
    • Leading to many many subclassifications, e.g. of asthma, breast cancer, obesity, of course diabetes (type 1 and type 2) and strokes (ischemic and hemorrhagic)…
  • Psychiatric classification: DSM-5
  • Blood types
• Psychology
  • Various proposed classifications of emotions
• Culture
  • Music
    • Musical genres
    • Musical instruments, especially percussion instruments
  • Food
    • Wines
    • Champagne
• Meditation
  • Jhanas
  • Maps of insight
• Dewey Decimal classification

A classification of classifications, if you will.

Sporadic elements include classifications of cars, demons, fairies, and swords.