What impression do you have of "Beowulf" after reading the poem?
It is difficult to tell if your question is asking for an impression of Beowulf the character or the entire poem. It is also difficult to tell if this question was meant for you, the student, to answer personally, or if you are curious about what others think. If this is a question posed by your teacher in class, let me highly encourage you to answer it as personally as possible. When teachers ask personal questions, most often, there is no correct or incorrect answers, but we really do seek to hear the actual opinions of our students.
With those thoughts in mind, I can tell you that the first time I read "Beowulf" on my own (before discussing it in class), I didn't like it very much. I was a sophomore in high school when I first read it, and at that time I wasn't especially appreciative of its age nor historical value. Rather, I'm quite sure I complained that the language was difficult to understand and that I wasn't particularly favorable toward "legend" stories. My English teacher at the time completely changed this initial impression, and my subsequent readings and teachings of the text have only heightened my appreciation of it.
First, it is noteworthy to me that "Beowulf" (the entire poem) serves as a foundational story for most of our modern hero stories. Beowulf, the character, is just believable enough to make him human, and someone we root for, but just super-human enough to make him legendary. As a character, Beowulf is in many ways, very much like any of our current superheroes (Superman, Batman, etc). He fights with honor and stands by his men no matter the cost. He possesses super human strength and courage which allow him to win battles against unspeakable odds, yet he remains mostly humble. Yet, he is suave, and knows how to respond to those, like Unferth, who attempt to discredit him in front of others. And because this story does not highlight any sort of love relationship between Beowulf and a woman, this character remains an eligible bachelor for the ladies to swoon over.
Once I was able to understand the language, I really liked Beowulf, both the story and the character, and I've found the general reaction from my students is much the same. Once they can get past the untraditional form and language (even when reading a modern translation), girls and boys alike tend to enjoy this text equally. The boys in my classes have often declared things like, "Finally, a story for us," yet even the girls find themselves rooting for this hero and appreciating the discussion that ensues.