Tape 100 like me, endlessly (8)
I believe the answer is:
cassette
'tape' is the definition.
(I know that tape can be written as cassette)
'100 like me endlessly' is the wordplay.
'100' becomes 'c' (Roman numeral).
'like' becomes 'as'.
'me' becomes 'setter' (the person that set this crossword).
'endlessly' means to remove the last letter.
'setter' with its final letter taken away is 'sette'.
'c'+'as'+'sette'='CASSETTE'
(Other definitions for cassette that I've seen before include "Music player" , "Container that holds a magnetic tape" , "Vintage recording" , "Container to go into tape deck" , "Spool of tape" .)