I've taken a list of English words, and examined each of them to see what they sound like (using the PHP metaphone function). This page lists the most common metaphone codes, along with their words. You can also search for a word of your own, and see which words sound similar - and which ones rhyme, and which ones alliterate.
supper super sipper sapper sappier soupier soppier speer supra spier spear speir zipper soaper zapper zappier zippier soapier seepier spar spur spry sapphire sapor spore spoor spiry spray spare spree sopor spire sprue sapour sparry spirea spurry sparrow spiraea spurrey
bopper pepper yapper tapper zapper whipper wrapper nipper supper rapper kipper dipper gipper dapper mopper sapper lipper lapper shipper hopper upper lopper topper whopper chipper chopper whapper mapper copper hepper popper ripper napper capper gypper sipper quipper knapper shopper zipper tipper hipper cupper per cooper whippier paper reappear hooper soppier papery loper lippier happier rapier pear popery dippier pauper peppier dupery peer coper keeper piper speir loopier leaper weeper cuppier quippier yauper cheaper shaper looper toper ropery dopier doper opera zippier typier mopery foppery soupier coopery zappier sappier appear raper napery tippier nippier spier aper wiper duper hoper apery pipier hyper heaper roper coppra moper japer hoppier gawper goopier cheeper copier japery mopier pappier reaper pere soaper viper hippier ropier pier loppier taper caper spear coappear soapier peeper roupier riper nappier deeper leper peri diaper gaper peppery chippier whooper gappier seepier coppery speer weepier choppier beeper super yawper
sup sappy soppy soup soupy supe