Not at all! (that's something you can say if somebody thanks you...)

Don't worry about using "thank you" too much. It's not possible in the English language!!

People will simply think that you are an extremely nice and polite person, which is a good thing.
They don't think that you are silly or anything like that.

It's true that you should vary it a bit though. Personally I don't thank people if the service was appalling, or there was some big problem that was essentially their fault. That is still extremely rude... Sometimes I just say "Allright, thanks" and leave.
That's probably to do with me being Swedish. Most English people would thank them anyway. Then they complain after they left...

If you are happy, you can say:

Thanks, that's great!
Perfect, thank you very much!

... and lots of variations of this.

Many thanks, is a way of ending an email.
It's slightly more polite than just "Thanks", but it's still in the tone of "Do it!" If you are asking somebody to help you, it's more polite (but not completely necessary...) to say "I would be very happy for your help with this" or "I hope you'll be able to help me" etc.
"Many thanks" is ok if you are typing something brief and you are in a hurry. I use it a lot in my work emails, when I am telling people what to do. For example:

"I would appreciate if you can make sure that this is finished before seven this evening; any delay beyond that would be create lots of problems. Please let me know if there is any problem with completing this by seven. Many thanks, Hanna"

For example, perhaps you want to ask the postman to remember to close the front door after he leaves. You could say

"Dear Postman, please remember to close the front door when you leave our building, as it gets very cold every time it is left open. Many thanks!"

You are being nice and polite, but you are still making it clear that he must close the door.

Hope that helped!