On the other hand, when someone reads "echo LOOK_AHEAD" they immediately know it's a constant and thus (a) global and (b)(more importantly) defined once and never modified by the code.

With "echo $look_ahead" there's no indication of that, and in the future another dev might add something that modifies $look_ahead's value and break other parts of the code, making for sneaky bug (which incidentally is why non-constant globals are so disliked ;))

$db is something different altogether, in my code I have a cheap Database class and each model creates a new one -- but it relies on the MySQL functions it uses to re-use the database connection. So in reality it's the same thing.

The problem with not using a constant where it's necessary is that you're communicating the wrong thing to someone else or even yourself 6 months down the line. You might want to re-evaluate what you see as "ugly code" especially if it changes how you write the code.

Not only that but depending what kind of db wrapper class you have you probably want it to be modified by the code that touches it. Sure you could pass it around, I guess it depends on how many people touch the code.

Personally I global the database wrapper, the user session class and config stuff (which yes I could use constants). Although if the code base I'm referring to wasn't 95% me coding I would probably consider using global less.