There are few rites of programmer passage as iconic as writing your first parser. You might want to interpret or compile a scripting language, or you might want to accept natural-language-like ...

Parsing algebraic expressions is always a pain. If you need to compute, say, 2+4*2, the answer should be the same as (2 + (4 *2)), not ((2 + 4) * 2) — in other words, the right answer is 10, not 12.