When I was looking at a dictionary the definition (in the English part) was given as
be [get] excited; 《口》be [get] worked up
What exactly these
 are referring to is unclear to me. From my understanding 興奮している would describe the state of being excited (or having become excited). If 興奮する describes the state of being excited then the usage of 興奮している would seem redundant.
Maybe a few quick examples would help clear this up (or what I believe they mean):
Don't get so excited, keep your cool etc. This doesn't mean 'don't be excited', it means 'don't become excited'.
In the above it is saying that his daughter was so excited that she mightn't've been able to see her surroundings.
This one says that saw the guitar one month ago. This caused him to become excited, which led to him buying it (I don't feel like translating the usage of つい or しまう here as they are not the focus).
So in #1 it was "don't become excited", #2 it happened because she was excited and in #3 it happened because he became excited. Is this right?
An additional example here:
I am very excited about the trip. と表現できます。
☞ 「わたしは～にとてもわくわくしています」は、I am very excited about ～ という言い方をします。
☞ <am + excited> は、「（わたしは）興奮する、わくわくする」という意味です。
☞ <be 動詞 + excited + about ～> は、「～に興奮する、わくわくする」という意味を表しています。
The boy was excited about the story. と表現できます。
They say that わくわくする、興奮する means <am + excited>. If this was the case then why wouldn't they just leave it at that?
In part one of that link they use the example ～に興味がある to mean 'to be interested in' and (obviously?) one does not use 興味があっている in this case (it seems there are some results on Google search for this but most are learner mistakes and I'm not checking the rest).
Anyone care to clarify things?