One of the staples of science fiction is the proposition that if we discover alien life in the universe, its intelligence and way of thinking will be very foreign to humanity and perhaps even incompatible or mutually inscrutable. I see no reason why this would be the case.
Human intelligence is very adaptive -- it adjusts to accommodate the reality of the universe around it. This property may be tautological in that "intelligence" that cannot comprehend or exist within the physical bounds of our universe can't really be considered "intelligence" at all. With that understanding, and assuming that our universe and its physics are homogeneous, it's hard for me to imagine that an alien intelligence would be very different from our own.
I've got no doubt that alien cultures, religions, motivations, and biology might be quite different from our equivalents, but I see no reason for them to think in fundamentally different ways. Unless their technology or physiology violate our current understanding of the laws of physics (being then "magic") they will be bound by the same general economic and moral constraints that we are. Their mathematics and science will mesh neatly with ours (even if they use a different notation) and their history and literature will fascinate us.
I think you're wrong on this one, Michael. Suppose that these aliens are similar to honeybees, ants, or spiders. We are primates, so we see the world and each other as primates.
We perceive certain wavelengths of light and sound, but nothing others. Our sense of smell is very weak. We form social groups and breeding pairs, but those social structures aren't very stable. Much of our thinking and history is devoted to ameliorating those instabilities, even though that instability is probably what makes our species so successful. Even the idea of sharing knowledge probably derives from our primate social instincts.
Orson Scott Card did a good job of envisioning insectoid aliens in Ender's Game. The aliens there thought nothing of vivisecting human space crews because they didn't expect that each member of our species would be an autonomous agent.
Most sci-fi is primarily rooted in providing a different stage on which to act out and evoke the various particulars of the human condition, of which Star Trek, Star Wars, the Stargate movie/series, and Battlestar Galactica are probably the best.
I've always been (and always will be) a Star Trek fan, myself. To me, it's always been the most fun and easiest to relate to, especially all the technical stuff mentioned and used throughout the movies and series: Heisenberg compensators, electro-plasma relays, hyposprays, holodeck, type 7 phase discriminator, decions, tetrions, gravitons, quantum torpedoes.. the list goes on and on :)
As for any non-fictional alien intelligences, I don't think there's any reason to anthropomorphize them.