Dreadlord, I hope the image Micheal kindly posted for me will give members a taste for Eomer slaying Ugluk. This was painted many moons ago using figures that appeared to look right for just a scene at the time. Now is an ideal chance to get an 'official' version.
I'm not sure if I agree with the idea that Eomer dismounted out of any respect for Ugluk (unless it says so), I would have thought it was simply an easier way of finishing this particular Uruk off.
I also think from Tolkien's point of view it just sounds a more romanticised way of despatching him when after all Eomer's horse could have done just as good a job with its hooves, but that wouldn't have read as well.
About Eomer being dismounted out of any respect for Ugluk : I don't think the dead of Ugluk was described in detail in LOTR, but I read it in a Tolkien lexicon (it says : Eomer made Ugluk a compliment by dismounting from his horse before killing him). Where the writer of this lexicon got the idea, I don't know, but I just like the idea and it shows some of the noble character of Eomer.