From the Haruhi Wiki.

It’s on many sites, but here’s a personal (literal) translation of the song Hare Hare Yukai (Bright/Cheerful Happiness), used as the ending song in the anime, Suzumiya Haruhi no Yuutsu (The Melancholy of Haruhi Suzumiya). A well known song in anime circles.

The Japanese is shown first, the translation follows. I wonder if I should provide romaji/all hiragana for others who just want to know how to say the words rather than the translation itself. Let me know.

—

Japanese 日本語で

ナゾナゾみたいに地球儀を解き明かしたら
みんなでどこまでも行けるね

ワクワクしたいと願いながら過ごしてたよ
かなえてくれたのは誰なの？

時間の果てまでBoo~~n!!

ワープでループなこの想いは
何もかもを巻き込んだ想像で遊ぼう

アル晴レタ日ノ事
魔法以上のユカイが
限りなく降りそそぐ　不可能じゃないわ
明日また会うとき　笑いながらハミング
嬉しさを集めよう
カンタンなんだよ　こ・ん・な・の
追いかけてね　つかまえてみて
おおきな夢・夢　スキでしょう？

イロイロ予想が出来そうで出来ないミライ
それでもひとつだけわかるよ

キラキラ光って　厚い雲の上を飾る
星たちが希望をくれると

時間に乗ろうよ
Boo~~n チープでクールな頃だもん
さみしがっちゃ恥ずかしいよなんてね　言わせて

手と手をつないだら
向かうトコ無敵でしょ
輝いた瞳には　不可能がないの
上だけ見ていると　涙もかわいちゃう
「変わりたい！」
ココロから強く思うほど　つ・た・わ・る
走り出すよ　後ろの人もおいでよ
ドキドキッ　するでしょう？

Boo~~n, ワープでループなこの想いは
何もかもを巻き込んだ想像で遊ぼう

アル晴レタ日ノ事
魔法以上のユカイが
限りなく降りそそぐ　不可能じゃないわ
明日また会うとき　笑いながらハミング
嬉しさを集めよう
カンタンなんだよ　こ・ん・な・の
追いかけてね　つかまえてみて
おおきな夢＆夢　スキでしょう？

English　英語で

If all the world’s mysteries were plotted on a globe,
anyone would be able to go anywhere

Wishing for excitement beyond our wildest dreams,
but who is the one who grants them?

Until the end of time! Boo~~n!

With a warp, this loopy feeling
mixes everything together in our imagination, playing with them

One sunny day
A happiness beyond comprehension
Will rain down without end, it’s not impossible!
When we meet again tomorrow, we’ll be laughing and humming
Let’s gather all the happiness
It’s really easy!
We’ll chase after it, we’ll try to catch it
You like big dreams, right, right?

Anything is possible in an uncertain future,
But I do know one thing for sure

Decorating the sky high above the thick clouds,
The sparkling stars give me hope!

Let’s ride time!
Boo~~n I’m at a cheap and cool age,
Allow me to express my loneliness and anxieties at times!

If we join hands,
We’ll end up invincible
In these shining eyes, nothing is impossible
Just by looking up, the tears will dry
“I want to change!”
Convey this strong thought from your heart!
Start running, the slower people left behind,
It gets your heart pumping, right?

With a warp, this loopy feeling
mixes everything together in our imagination, playing with them

One sunny day
A happiness beyond comprehension
Will rain down without end, it’s not impossible!
When we meet again tomorrow, we’ll be laughing and humming
Let’s gather all the happiness
It’s really easy!
We’ll chase after it, we’ll try to catch it
You like big dreams, right, right?

—

I took some liberties with some words here and there to make it flow a little better, however it has not been adjusted to flow as a song in itself, as that would take someone with the skill in song lyrics in English, too! But I hope this translation finds some use.

I found the kanji lyrics for this on a dedicated song translation site, but did not read their translation until after I had translated it myself.

For those interested, details on the show/light novel series can be found here.

The song, Hare Hare Yukai, can be heard/watched here, or viewed below: