The readability point is a fair one. It could help others when reading your code. Also possibly for hacking reasons it may help as you say. I don't really think about that as I would consider it high praise for someone to bother hacking anything I have done.
The tax calculation I cannot see as an advantage however. I would want the tax rate to be definable in the interface, so it wouldn't be a constant at all. It wouldn't be a very versatile program to have to edit the code to change a VAT rate. Just a variable that can change as needed, either from user input or an update.
I welcome any other examples. I am a little old fashioned with my coding style, and tend to use subroutines rather than functions, so there are quite possibly a lot of ways they may be useful in that way. When I first started using DB I was used to plain a=a+1. The inc command seemed fairly superfluous, but as I used it more I got used to it. Now with AppGameKit I feel as if I have gone back to the stone age having to use the old formula, although it works exactly the same way
Edit- another post inbetween lol. The true and false argument is again based on readability, so fair enough, although I automatically treat 1 and 0 as on or off or true and false anyway. But as the sole coder I would know not to change the relevant variables anyway.
For colours I would simply use "red=rgb(255,0,0)", as long as I don't change red it will stay the same. Ditto for keystates or any value I would want to keep the same.
Your last example using types seems a good one, apart from I do not use types at all. I find once I start getting into the thick of it, it is far easier to use a standard array than a typed one. Again readability is not good (you have to know what all the numbers mean), but code wise it is sound.
Thanks for the detailed reply, nothing has convinced me that constants are half as useful as people make out yet, but I am at least learning a little about how people use them to aid their own programming styles. I also think the hacking argument is the best so far

Although for instance say you set up lives as a constant, so no-one can hack it to a different value, you would still need a temporary value in game ( so you can lose or gain lives). So I can only see it being of limited use even for that.
http://s6.bitefight.org/c.php?uid=103081