Zenkei Shibayama, The Gateless Barrier: Zen Comments on the Mumonkan (Shambhala, 2000)

Yamada Koun, Gateless Gate (Wisdom Publications, 2004)

Robert Aitken, The Gateless Barrier: The Wu-Men Kuan (North Point Press, 1990)

All three are translations of the Chinese collection Wumenguan (Japanese Mumonkan); they include contemporary commentaries on each koan, which make them a good place to begin exploring the tradition

Thomas Cleary and J.C. Cleary, The Blue Cliff Record (Shambhala, 1992)
The Chinese Biyan Lu (Hekigan Roku), associated with the Linji (Rinzai) school. It was compiled in the 11th century by Xuedou, who added his own verses and remarks. In the 12th century, Yuanwu added introductions and commentaries. Dense, poetic, and sometimes perplexing, it's considered by many to be the richest and most challenging koan collection

Thomas Cleary, Book of Serenity: One Hundred Zen Dialogues (Shambhala, 1998)
The Chinese Congrong Lu (Japanese Shoyo Roku), associated with the Caodong (Soto) school, compiled in the 12th century and including introductions, commentaries, and verses for each koan from that time

Gerry Shishin Wick, The Book of Equanimity: Illuminating Classic Zen Koans (Wisdom Publications, 2005)
Versions of the koans based on Maezumi Taizan's translations, with commentaries by Gerry Shishin Wick

Thomas Yuho Kirchner, Entangling Vines: Zen Koans of the Shumon Kattoshu (Tenryu-ji Institute for Philosophy and Religion, 2004)
A rich collection of 282 koans, many not found elsewhere, with the original Chinese and extensive scholarly notes

Yoel Hoffmann, Every End Exposed: The 100 Koans of Master Kido (Autumn Press, 1977)
A translation of this Rinzai classic by the Chinese teacher Xutang (Kido), with comments by the Japanese teacher Hakuin. Perhaps more than any other collection, this one says: Here is an instance of freedom, and here is another one, and another

Francis H. Cook, The Record of Transmitting the Light (Center Publications, 1991)
A translation of the Japanese Denko Roku, written by Keizan Jokin in the early 14th century; it presents a legendary Zen lineage from Shakyamuni through Dogen, telling the enlightenment story of each ancestor in the form of a koan, with added biographical material and commentary

Trevor Leggett, Samurai Zen: The Warrior Koans (Routledge, 2003)
A collection of Japanese koans from the Kamakura era (13th century), including traditional poems and checking questions; one of the best sources for koans involving women

Victor Sogen Hori, Zen Sand: The Book of Capping Phrases for Koan Practice (University of Hawai'i Press, 2003)
The most extensive collection of capping phrases, brief original writings or quotes linked to a koan by a commentator or someone doing koan study; includes a detailed description of contemporary koan practice in Japan