These puzzles involve manipulations of words and often the letters within words, but not in a crossword-like way.
7 Little Words (online word game)
acronyms
adding "in bed" to fortunes
alliteration
alphabetic sequences
alphabet subsets
anagrams
analogies
anaquote
___ and ___ phrases
Anguished English
ascending and descending letters
backswitch
before and after
black box (solver must figure out inner workings)
Bulls-Eye 20 Questions
cartoon rebuses
charades
common letters
consonantcies
cryptic crossword clues
deletions and insertions
discover the hidden rules
double letters
dropquotes
Equation Analysis Test (26 = L. in the A.)
eye rhymes
false comparatives
false negatives
false plurals
flats (NPL puzzles)
following directions
German sausage puzzle
goroawase
heteronyms
hidden words
hill words
homonyms: see homophones
homophones
interleaved words
jigsaw quote
Jumble puzzle
knight's tour
laddergrams
letter adjacency graphs
letter banks
letter changes
letter links
letter shifts
letters in same positions
lipograms
mangled clues
misspellings
Namystics
numbers associated with or in words
odd man out
palindromes and palindromic sequences
pangrams
paragraph puzzles
phonetic letters and numbers (NV = envy or single letters)
phonetic puzzles
printer's devilry
puns
quotation puzzle: see dropquotes
quotefalls: see dropquotes
quote square
rebus
reduplications
repeated letters
reversals
rhyme schemes
rhyming words
riddles
rotated letters
Scrabblegrams
silent letters
solitaire hangman puzzle
sound changes (phonetic letter changes)
spoonergrams: see spoonerisms
spoonerisms
supervocalics: see vowels, phrases containing all
things shaped like letters
Tom Swifties
transdeletions and transadditions
transpograms
trigrams
unistems
valley words
vertical anaquote
vowels, phrases containing all
wacky wordies
Waterfall puzzle
Wheel of Fortune
Word Avalanche: see reduplications
word chains
word deletions
word functions: see discover the hidden rules
word ladders
wordplay (other)
word stack
word substitutions