Assonance: Figure of repetition in which different words with the same or similar vowel sounds occur successively in words with different consonants; two or more words with similar vowel sounds sandwiched between different consonants.

Examples

"As I was going to St. Ives, I met a man with seven wives, 
Every wife had seven sacks, every sack had seven cats, 
Every cat had seven kittens: kittens, cats, sacks and wives, 
How many were going to St. Ives?"

-- delivered by Jeremy Irons, from the movie Die Hard with a Vengeance (as taken from the riddle poem "As I was going to St. Ives")

Note: Also Alliteration

-- Johnny Cochran, Closing Arguments from the O.J. Simpson Trial

"In this day and in this hour, when we are looking for the right words to say, it is good to turn to a prayer that was taught to us 2000 years ago. When Jesus told his disciples to pray for the kingdom, to pray that the kingdom might come on earth as it is in heaven, this was no pie in the sky by and by when you die kind of prayer."

-- Tony Campolo, Remarks at the 1997 Inaugural Interfaith Prayer Service

-- delivered by Harry Connick, Jr. (from the movie Independence Day)

"In the brief span of thirty-odd years, the world has seen an inventors dream, first materialized by the Wright brothers at Kitty Hawk, become an everyday actuality."

-- Amelia Earhart

"We must forgive each other, redeem each other, regroup and move on. Our flag is red, white, and blue -- but our nation is rainbow. Red, yellow, brown, black, and white, we're all precious in God's sight."

-- Jesse Jackson, 1984 Democratic National Convention Address

Maverick: "Yeah."

Maverick: "What's that?"

Maverick: "Really."

Maverick: "I feel the need --

Maverick and Goose: -- the need for speed."

-- delivered by Whip Hubley, Tom Cruise, and Anthony Edwards (from the movie Top Gun)