Helloellolloloo Worldorldrldldd

brainfuck, 60 56 bytes

,[>++++++++[-<----<++++>>]<[>>]<[[<]>.[[-]>[.>]<[<]>]],]

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Requires a trailing space and prints a leading space. Both of these could be circumvented, but that ends up at 112 bytes.

Explanation

,[  Loop over each byte of input
  Tape: 32 w o r-32 d'
  >++++++++[-<----<++++>>]   Subtract 32 from the character and add 32 to the previous char
  Tape: 32 w o r d-32 0'
  <[>>]<   If the last character was a space
  Tape: 32 w o r d-32 0'
  or
  Tape: 32 w o r d' space-32
  [
    [<]>.   Move to the end of the word and print out the space
    [   Loop over each letter
      [-]    Remove the first letter (initially space)
      >[.>]  Print the rest of the word
      <[<]>  Move back to the first letter
    ]
    Tape: clear
  ]
,]  Get the next byte of input

Japt -m, 6 3 bytes

Input and output are arrays of words.

£sY

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---

Explanation

        :For each word in the input array
£       :Map each letter at index Y
 sY     :  Slice the current word from index Y

Haskell, 36 21 bytes

map$concat.scanr(:)""

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Edit: -15 bytes, because of new IO format (list of words instead of space separated words)