The following are not excluded by the hearsay rule, even though the declarant is available as a witness:
(2) Excited utterance. A statement relating to a startling event or condition made while the declarant was under the stress of excitement caused by the event or condition.
The basic idea behind the excited utterance rule is that these types of statements tend to be such good evidence that we'll let them in even though they're hearsay.
With hearsay, you generally double the unreliability of any evidence. Tom ran the red light, said on the witness stand is good evidence. Somewhat unreliable, because maybe the witness is mistaken, or biased, or Andy Kaufman, but still pretty good. Hearsay compounds these problems. Jill said Tom ran the red light. Well, the court can't see Jill's demeanor, judge if she's lying, or an idiot, so we don't let it in.
But, an excited utterance, like many of the exceptions, eliminates this concern. Holy rapture! Tom just ran that red light! Well, odds are the declarant (the dude who uttered excitedly) honestly blurted out whatever he observed. And, since this tends to be an eye witness speaking on point, that makes this really important evidence, and with concerns about its accuracy lessened, though not eliminated, we let it in.
An excited utterance doesn't need to be made right at the moment, but just under the feeling of excitement. The declarant, having just witnessed a horrific three car pileup, might talk to a police officer 15 minutes later, and still be shaken up. What you're really looking for is the excitement (so to speak) of the event overriding the ordinary person's tendency to scheme, or embellish, or forget.
And yes, this does mean that if you had some conspirators, you could work into trial some great testimony. But, that would be unethical, so don't do it!
Note that this is hearsay, but not excluded. That's different from things that look like hearsay but aren't.