Mild:
* Content
* Satisfied
* Delighted
* Gratified
* Glad
* Happy
* Amused
* Cheerful
Strong:
* Thrilled
* Elated
* Ecstatic
* Jubilant
* Overjoyed
* Rapturous
* Enraptured
* Exhilarated
Other possibilities:
* Formal: Fulfilled, gratified, contented, satisfied, agreeable
* Informal: Tickled pink, over the moon, stoked, beaming
* Specific: Proud, relieved, grateful, impressed, inspired
Consider these questions:
* What is the context? Is it a formal or informal situation?
* What is the intensity of the emotion? Are they mildly happy or over the moon?
* What is the specific reason for their happiness? This might suggest a more precise word.
For example, if someone is happy about a promotion, you might say they are thrilled or elated. If they are just happy with the weather, content or pleased might suffice.