I love this quote by 3 time Boston Marathon winner Robert Cheruiyot that I snatched from boston.com:
“When the lion is chasing the antelope, he doesn’t look back. He has to eat,” Cheruiyot said. “So when I run, I don’t stare at my time.”
Dude was focused on winning the race and wasn’t going to waste energy worrying about his splits or finish time, particularly in the very harsh conditions the Boston Marathon was run in yesterday. He knows where his bread is buttered.
Can you relate to this? What do you think about when you’re racing? Do you look back? Or do you want to eat?
One thing you can count on– if I’m there, I’ll be hungry. 
I definitely understand that philosophy – unfortunately I’m not experienced enough yet to abide by it. If I don’t watch my splits my race suffers (and so do I:)!
I think about the task at hand – time is irrelevant, only check it for eating/drinking purposes. All that matters – are you ahead or behind? If behind, you better catch up. If ahead, you better keep running like heck!
I’ve found that split markers are just as often incorrect as they are correct (see my “almost 10k race report”), and if there are hills, the splits won’t be even anyway, so why concern myself with whether I’m hitting a certain number or not, if it’s right or not, etc? I’ll look back at my splits later and assess then– but the time for that is NOT during the race. During the race, I RACE.
In fact, I use a GPS that doesn’t even show average speed on the bike, and only shows current speed in min/mile– I focus on form and perceived exertion– am I where I should be? Should I be doing more?
Like Elizabeth said, for fueling purposes, I watch some numbers, but I usually pick some mileage points as targets instead of time-based. Has worked OK so far.