I'm wondering if there has been research into whether users actually enjoy receiving those 'We got your email' type of responses from support requests or feedback forms. I find it irritating personally, but I realize I could be in the minority.
This type of system behaviour is an implementation of a Feedback Loop, which is key for interaction design.
In Seductive Interaction Design, Stephen Anderson summarises:
In this specific case, you can argue that a sufficient feedback loop would be to display an on-screen message saying: "We have recorded your request and will get back to you in due course."
However, confirmation emails have some additional benefits:
You can make an analogy here to a launderette receipt - would you prefer the owner to just tell you "It's alright Sir - I've got your name and telephone in my books; no need for a receipt. Just come back on Wednesday"?
Having said that, none of this may apply in your situation, and the benefit of such emails may outweigh the cost (of users having to deal with these emails).
Like receipts, if your reckon there may be too many too frequently, offer your users the option to opt out. Doing so would also answer your question - as you will have analytics regarding how many people, like you, find it unnecessary.
As confirmation emails are an overhead that people have to spend time and resources dealing with, the potential for annoyance is high.
When they function as feedback to an action then they are problematic because they are neither close in time to the action, nor close in location (you have to be logged in to your email account to check for, or be alerted to, the confirmation email).
When they function as receipts (i.e. in the types of processes that typically require receipts) they are more suitable. Consider though that when they serve primarily a "peace of mind" or "insurance" function (where they are only needed in the case of a breakdown of the process) they will cause the user to spend time and resources dealing with an email that is unnecessary the vast majority of the time.
So an analysis of the task and process is needed to determine their suitability.