There are many racial slurs out there but the term Eskimo, used for the people now referred to as Inuit (as they in fact most often call themselves), is technically not one of them. After reading various posts and letters in online forums on the issue, I can see that the word Eskimo has been blown out of proportion from an innocent exonym to something that people will defend against with fists flying. (I just find it oh-so-ironic when mental zombies who use political correctness to gain attention end up misrepresenting human compassion and facts with this sort of culturally divisive lexical war so let's get this out in the open, shall we?)
The word is not of European origin; we know that much. It has been purported to be derived from an Algonquian word (possibly from the Abnaki language: askimo) meaning 'raw meat eater', although other scholars refute this etymology and offer another alternative involving the Montagnais term aiachkimeou /a:jasʧime:w/ or its Cree counterpart askimew both meaning 'snowshoe-netter' (even though snowshoes were hardly a distinguishing feature of the Inuit in contrast to any other aboriginal peoples of Canada). People will often just assume a priori that the dreaded White Man invented the word but while many European immigrants have done much harm to First Nations peoples over the centuries, the origin of this word is in one way or another squarely Algonquian. This ethnonym dismays a lot of people though and it probably has to do with the mistaken belief that its meaning is somehow in itself insulting. Yet, let's allow ourselves to think about this controversy for a second. Do the Inuit eat raw meat? Why... in fact, they do! So if it's just a simple observation that Inuit happen to eat a lot of raw meat, why the insult? Perhaps witiko-psychosis adds something to this perception of derogation (i.e. witiko is the Cree term for 'cannibal' as well as a mythical monster who eats humans as if they were 'raw meat' or askiwiyas). To add to the complication however, not all Eskimo-Aleut speaking peoples find the term Eskimo insulting at all.
What have we learned from this? Well, aside from the fact that human beings are worrying too much about political correctness to see the forest for the trees, Eskimo carries no direct racial or cultural insult. However it happens to be insulting for some more because of modern history and cultural politics than anything. Regardless of politics though, the term Eskimo-Aleut remains the term of choice for linguists to refer to the language family with which Inuktitut, Yupik and Aleut are affiliated.
 Strong, Captive selves, captivating others: the politics and poetics of colonial American capitivity narratives (1999), p.37 (see link): "The English word Eskimo derives from a pejorative Algonquian term meaning 'raw meat eater,' and Inuit is the preferred term in the Eastern Arctic."
 Bastian & Mitchell in Handbook of native american mythology (2004), p.xii (see link) assert that the 'eaters of raw meat' hypothesis is incorrect: "Many Inuit regard the word Eskimo as pejorative, in part because it was long thought, erroneously, to mean literally 'eater of raw meat.'" The etymological controversy is also mentioned by Archie Hobson on page 160 of The Oxford Dictionary of Difficult Words (2001) but details why it's not derogatory as commonly believed: "In recent years Eskimo has come to be regarded as offensive because of one of its possible etymologies (Abnaki askimo 'eater of raw meat'), but this descriptive name is accurate since Eskimos traditionally derived their vitamins from eating raw meat." Finally, another alternative etymology is suggested in Hirschfelder/Beamer, Native Americans Today: Resources and Activities for Educators, Grades 4-8 (2000), p.3: "Some linguists argue that the word originated with the Montagnais and actually means 'snowshoe netter.'" To be precise, the Montagnais term was originally used instead for the Micmac, not the Inuit.
 Artibise, Interdisciplinary Approaches to Canadian Society: A Guide to the Literature (1990), p.117 (see link): "There are three Eskimo languages, but the only one in use in Canada is Inuktitut, and in that language the word for 'people' is 'Inuit,' a term which became a standard for the Eskimos of Canada after it was selected for the title of their major political organization, the Inuit Tapirisat of Canada. There is nothing derogatory about using the word 'Eskimo,' and it is still the conventional term in Alaska."
 Bastian/Mitchell, Handbook of native american mythology (2004), p.xii (see link).