Every Japanese high-school graduate is expected to have learned a set of 2,136 kanji called the Jouyou kanji, which covers the majority (but not quite all) of the kanji in common use today. Mastering this entire list is a difficult feat that many foreigners never accomplish. As a casual student of Japanese I personally am only familiar with a few hundred of the most common.
There are also thousands and thousands of historic kanji that have basically faded from modern Japanese and only show up in historic documents and certain names. There really isn’t any reason for your average American student to worry about these. In fact, most Japanese aren’t really that familiar with the older kanji either.
Anyways, don’t obsess about memorizing kanji too much. You don’t have to read kanji to speak Japanese and a lot of entry level Japanese literature has hiragana pronunciation guides called furigana printed right next to every kanji symbol. Even more complex texts tend to have furigana for uncommon kanji so you really don’t have to memorize all the kanji all at once to start enjoying basic Japanese stories and comics.
可愛い =かわいい= cute
恥ずかしい = はずかしい = embarrassing
Always A Silver Lining
Yellow: I’m tired of dictionaries. Maybe I should just memorize all the kanji.
Blue: Good luck. There are several thousand.
Yellow: Several thousand!!
Blue: Don’t worry. Modern 日本語 only really uses about 2,000 of them. The rest are pretty uncommon.
Yellow: That’s still too many! Especially since this 制服 isn’t making 日本語 any easier.
Blue: Did you really think it would?
Yellow: Oh well. At least it’s 可愛い.
Blue: I think the word you’re looking for is 恥ずかしい.