From The Complete Rhyming Dictionary by Clement Wood:"Rhyme is the identity in sound of an accented vowel in a word...and of all consonantal and vowel sounds following it; with a difference in the sound of the consonant immediately preceding the accented vowel. If a poet commences, 'October is the wildest month' he has estopped himself from any rhyme; since "month" has no rhyme in English."

The following is a list of English words that are difficult to rhyme (the rhyming word is foreign, dialectical or obsolete) or have no true rhyme at all:

Word     Rhyme
aitch     brache , taich
angry     unangry
angst    
breadth    
bulb    
carpet     charpit
chimney     timne, polymny
cusp     wusp
depth    
eighth    
else    
exit     direxit
fiends     teinds, piends
filched     hilched, milched
filth     spilth, tilth
fifth    
film     pilm
fluxed     luxed, muxed
glimpsed    
gospel 
golf   
gulf    
jinxed     outminxed (?)
leashed     niched, tweesht
liquid    
mollusk    
mouthed     southed
month    
mulcts    
mulched     gulched
ninth 
nostril   
oblige    
oomph     sumph
orange    borange
pint     jint
poem     phloem, proem
pregnant     regnant
purple     curple, hirple
puss     schuss
rhythm     smitham
scarce     clairce, hairse
sculpts    
silver     chilver
sixth    
spirit     squiret
tenth     nth
tsetse     baronetcy, intermezzi
tuft     yuft
twelfth    
width    
window     indo, lindo
wolf