Looking for a different word to use than 'Dear'

You could use "good morning," "good day," or "Merry Christmas" (depending on the setting). "Greetings," "salutations," and "hello" might also work. "Dear" seems to be the best and most formal, however.

From comments:

I almost always skip the "dear" or equivalent altogether. That is, instead of "Dear X," I simply write "X,". I'm a white collar worker in corporate America, and my experience is that "Dear" is almost never used, and when it is, at best it's taken as stilted and out of place, and at worst as outright sycophantic. [This is all in the context of American b2b communication, both internal and external, but I can't speak for b2c communication or BrE or other non-AmE norms.] -- Dan Bron

In contrast to Dan's comment, I can say I have never received a 'formal letter for business purposes' which did not start with 'Dear' - either 'Dear Sir', Dear Peter, or Dear Mr G. - This is BrE. The perception of an affectionate tone is . . well, 'Dear Sir, Unless . . . ' as a starter to a most unsettling communication is a bit of a cliché, so I guess, just that - a perception. Emails are a very different matter; no solid convention seems to have crystallised yet. -- PeterG

In a formal business letter, using Dear xxxx is a formula; it doesn't have any value/denotion/connotation of affection associated with it. -- Arm the good guys in America