JMdict combines the results of several research projects to determine whether or not a word should be counted as “common”. There are currently 15,572 words on this list that include at least one kanji character. Out of the 1,945 standard Jouyou kanji, 1,894 show up. The 51 rare ones are listed below:

舟 悦 抄 附 殉 禍 硝 酌 鋳 錬 剛 頒 芳 薫 尼 庸 廉 逝 遵 某 貞 滋 墾 蚕 侯 仙 孔 吏 嗣 謁 宵 丙 壱 弐 升 匁 勺 隻 脹 坑 痘 曹 恭 詔 朕 錘 銑 塑 虞 繭 璽

Of course, if you’ve mastered the other 1,894, it seems pretty silly to ignore these, especially when there are 576 non-Jouyou kanji on the list:

其 此 頃 惚 呆 呂 剥 袖 脇 拭 兎 儲 伊 鹿 馴 霞 雀 闇 蜜 蔑 苛 苑 胡 纏 繋 籤 瓜 爪 濡 潰 溜 洒 旦 掻 捻 戴 憧 宛 塵 吃 叩 凄 儘 俄 鱈 鬱 骸 馳 餅 頬 須 韓 雛 隙 阪 鍋 錆 迄 辻 輿 跨 賭 賑 貪 謎 誰 詫 蝶 蜂 藤 薩 薔 薇 蕎 葵 葛 萩 萎 艶 臆 股 耶 綻 綴 籠 箸 稽 禿 碌 眩 眉 痺 痕 痒 瓦 狙 犇 煽 烏 汲 汎 槌 椅 梯 柏 暢 暈 斐 擽 揉 揃 捲 挫 拳 拉 或 徨 彷 巾 屑 屏 尻 尤 妬 妖 塞 噛 噌 嘘 喧 喋 呪 吊 叶 只 匂 勿 剃 僻 俯 仄 亀 乍 乃 丼 齎 鼾 鼠 黴 黍 麺 麹 麟 麓 麒 鹸 鷹 鷲 鶴 鴨 鳩 鰻 鰯 鯵 鯛 鯉 鮪 鬘 髭 騙 駒 饉 饂 餡 餌 餃 飴 飩 颯 顎 頷 頓 頁 韆 鞦 鞄 靨 靡 雁 隼 隈 阿 阜 閾 閏 閃 鐵 鎌 鍵 錫 錨 錦 鋸 鋏 銚 釜 釘 醤 醒 酎 那 遽 遥 遡 遜 逞 這 迦 迚 辿 辰 轢 軈 躾 躓 躊 躇 蹴 蹲 蹌 踵 踉 跪 贔 贅 賂 貶 貰 貌 讐 謳 謂 諺 諦 諄 詣 訣 訛 覗 襖 襁 褪 褓 褄 裾 袴 蟻 蟹 螺 蝿 蝕 蝋 蝉 蜻 蜘 蜀 蛸 蛛 蛙 蛋 蛉 虹 虎 藍 藁 薐 蕾 蔭 蔓 蓮 蓙 蓋 蒙 蒔 葱 葡 萌 萄 菩 菠 莫 荻 茹 茸 茣 茄 苺 苔 芯 舵 舐 舅 臥 臍 膳 膝 腺 腫 腎 脛 脆 肘 聳 聊 耽 翔 羨 罹 罵 罠 罅 縺 縞 縋 縊 緞 絨 絆 紐 糺 糊 粥 簾 箪 箒 箋 筐 筈 笹 笥 笠 竿 窶 窄 稍 稀 秤 禄 祇 磯 瞼 瞳 瞭 瞑 睨 睦 皺 皰 癌 瘤 痩 痣 疹 畿 畏 甦 甥 璧 瑞 瑚 琶 琵 琲 琢 珊 珈 玩 獅 猪 狼 狡 狐 牙 牌 爽 爺 燵 燭 燕 熊 煎 煌 煉 焜 焚 焉 炬 炒 灘 灌 澱 漕 漑 滲 溺 溢 湧 渾 渚 淵 淀 涎 浚 沙 汰 氾 殆 歪 櫛 檻 檎 橙 橘 樽 樺 槍 楷 楯 楠 楕 楊 椿 椒 椀 棲 棘 梨 梁 桶 桐 桂 桁 栗 柿 柴 柑 枕 杜 杖 杏 李 曙 曖 晦 晒 昧 昏 旁 斡 斑 敲 撰 撫 撥 撒 摸 摯 揶 揄 掴 掬 掟 掏 捩 捧 捗 挽 挨 拶 拵 戚 愈 惧 惣 悉 恰 怯 忽 彦 彙 弥 弛 弄 庵 庇 幡 巽 巴 巳 嵐 嵌 崖 峙 屹 屡 屓 屁 尖 寅 宥 孰 孕 嬉 嫋 嫉 婉 娼 姪 姑 奢 夥 壕 堰 堆 埃 垢 囁 囀 嚏 噂 嘸 嘴 嘲 嘩 嘗 嗽 嗟 嗅 喩 喉 唾 唸 唄 哨 咳 咎 咄 呟 吠 叱 卿 匙 勾 剪 凭 凧 几 凌 凋 冴 兜 儚 僑 僅 偖 倶 俺 俣 俎 侶 佇 佃 伎 些 也 乞

What this little bit of late-night script-hacking really demonstrates (if anything) is that the Jouyou kanji selection is actually pretty good, with only a few “useless” characters, only one of which is taught as part of the 1,006 grade-school set (蚕 = silkworm). The Kanji In Context books also fare pretty well in this test; only one “useless” character is among the first 1,000 taught (舟, a variant of 船 = ship), and more than half are among the last 100.