General synonyms:
* Enthusiastically
* Eagerly
* With gusto
* With zeal
* With passion
* With fervor
* With animation
* With vivacity
* With exuberance
* With delight
* With joy
More specific synonyms:
* For a person: thrilled, elated, ecstatic, rapturous
* For an action: impatiently, impulsively, frantically, feverishly
* For a feeling: eagerly, longingly, anxiously (if the excitement is tinged with worry)
The best synonym will depend on the specific context and nuance you're trying to convey.