A solidly built kitchen island attached to the kitchen floor is a built-in; a mobile kitchen island from IKEA is not.
A trimmed, anchored bookcase is a built-in; a freestanding bookcase is not.
Built-ins can be very personal. Built-ins speak to the owner's love of reading by a window (built in window seat); collecting old books (built-in bookcase); keeping bathroom items tidy (medicine cabinet); displaying prized collectibles (wall niche). By the same token, built-ins are often the first to be removed when a subsequent buyer takes over the house. I have removed my share of weird cabinets and cubbyholes from previous owners.
But if you design and construct your built-in right, you increase chances of them becoming tightly-knitted features of the house--features that only enhance the house.
Built-ins are rarely necessary. Instead, they are "fun" remodels you get to do after you've done the hard stuff.
These are 7 of my favorite projects from Black and Decker The Complete Guide to Built-Ins: