It very much depends, and I'll refer you to
HomeSkool's Guide to Letters of Intent for a comprehensive treatment of the issue. But here's the general gist:
- Most LOIs aren't worth the time it takes to write them. Adcoms generally assume they're insincere and many (most?) schools won't even take a second look at them.
- An LOI will only be worth something if you've been accepted to a school that's more prestigious than the one you're sending the LOI to. An acceptance to Saint Louis University won't impress OHSU, and an OHSU acceptance probably won't sway Harvard.
So think hard before sending an LOI and make sure it's something that will actually help you. And remember that an LOI almost never has any weight unless you tell them which school(s) have already accepted you.