Counter for thin, flat objects (sheets of paper, plates, coins, tickets, etc.).
写真を一枚アルバムに入れた。
I put one photo into the album.
紙を何枚必要ですか？
How many sheets of paper do you need?
この皿は二枚で千円です。
These two plates cost 1,000 yen.
Counter for portions of certain foods (e.g. plates of gyoza or soba) — usage depends on the dish or restaurant custom.
こちらの餃子は一枚が八個入りです。
This plate of gyoza contains eight pieces.
そばを二枚追加で頼んだ。
I ordered two more servings of soba.
In sumo, a counter used for ranks/positions on a ranking list (e.g. '--th position' on the banzuke).
彼の名前は幕下二枚目に載っている。
His name appears at the second makushita rank on the banzuke.
番付で十枚目に名前があると昇進は難しい。
Being tenth on the banzuke makes promotion difficult.
In sumo, a counter for the number of wrestlers belonging to a particular rank.
今場所は幕内に西の力士が十枚いる。
This tournament there are ten makuuchi wrestlers on the west side.
関脇は通常左右合わせて二枚いることが多い。
There are usually two sekiwake (left and right) — counted as two wrestlers.
Counter for fields or rice paddies (plot of land). This is an older or regional usage.
祖父は家の周りに田を三枚持っていた。
My grandfather owned three plots of rice field around the house.
昔は一枚の田で家族が暮らしていた。
In the past a single rice field plot could support a family's livelihood.
Counter for palanquin bearers (historical/literary usage).
駕籠を抱えるには四枚の担ぎ手が必要だと記されている。
It is written that four bearers are needed to carry the palanquin.