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茶入（ちゃいれ）
Excellent link describing the different shapes.
肩衝（かたつき）
- 油屋（あぶらや）, which was 不昧's most beloved one.
大海（たいかい）
Flat 茶入 with big opening. Means open sea, because the tea when seen through the opening looks like the big sea between Japan and China 1). It's supposedly what 栄西（えいさい）used to bring in tea seeds from China.
It is normally used with a 長緒私服（ながお しふく）. I saw this on 8 I 18 with 高橋先生.
