I'd like to focus on two main conflicts in Lord Tennyson's "Ulysses": responsibility vs. the thirst for adventure, and ambition vs. old age.

Let's start with old age. Tennyson's Ulysses is an aged king long past his prime. He's old and (presumably) infirm, far removed from his days of warfare and adventure. Despite these qualities, Ulysses still has ambition to travel to far-off lands and perform courageous deeds. Ultimately, ambition trumps old age, as Ulysses ends the poem by setting off for unknown territory.

Additionally, there's the conflict of responsibility vs. the thirst for adventure. Ulysses is a king, and so he has a responsibility to stay in Ithaca and provide for his subjects. Furthermore, he's a husband and a father, and so he has familial duties on top of his political concerns. However, Ulysses clearly resents these responsibilities, as they hold him back from fulfilling his love of exploration. Adventure proves to be more important for Ulysses than his many responsibilities in Ithaca, and some readers might argue that this fact makes Ulysses an unlikeable and selfish character by the end of the poem. Such an opinion would certainly be justified.