If G-d is so great, why does He need us to praise Him in our prayers?
You are correct - G-d does not need our praise. Indeed the prayers are not for G-d but for us! Prayers are part of an amazing system which G-d has established in order to bring man to his ultimate moral perfection and elevation. To state simply a deep topic, with many branches and ramifications: When G-d wants to elevate a person from his “drowning” in the day-to-day material life, one of the ways He uses is to bring upon him events or sufferings which cause him to call out to G-d in prayer.* When he does so, he already rises above the mundane world where man follows his material desires or thinks he is in charge. In prayer he realizes/remembers that his life depends on the Source of Life and thus turns to Him. In prayer he enters the world of loftier ideals and concepts that he had forgotten or was too busy to think about. When tragedy or illness befall him he is “forced” to reconsider them. Thus through prayer man has elevated his spiritual-moral existence. And since that was the goal of the tragedy or illness, it now goes away, no longer being necessary, having fulfilled its purpose.** .The prayer is answered! Thus prayer is not for G-d, but for us, facilitating our refinement. This also explains the famous question of how prayer effects changes in G-d. Again, prayer causes no changes in Him but in us, we being raised to a higher level where we then “deserve” a different Divine guidance. * This is not the only reason there is suffering or disease, but one aspect in reference to prayer. ** Since G-d does not bring suffering without a purpose. References: Rabbi Avraham Yitzchak Kook, Eyn Aya - Commentary to the Talmudic Agada – Shabbat Vol. I, p. 27; Olat Riyah – Commentary to the Siddur Vol. I, p. 24ff. Maharal of Prague, Netiv HaAvodah, ch.3