For the past 4 years or so, I've worked without ever having a clock in sight. I don't wear a watch, I removed the clock from the menu bar of my computer, and I cover up any clocks I can't remove. I realized that watching the clock, even subconsciously, is stressful. You're always aware of the time ticking by, wondering if you're getting enough done or if it's time to eat lunch yet. But you can't fully focus if part of your mind is keeping track of the time, so I decided to experiment by going clockless. Four years later, and there is no going back. Sure, sometimes I accidentally forget to eat lunch, or stay up until 3am when I meant to go to bed at 10pm, but I think of that as a feature, not a bug. If I was able to skip those things without noticing, I was probably in the zone, and 3 hours of zone time is equivalent to about 8 hours of fractured time, so it's well worth the trade.
I only recently came across this quote:
I owe my success to the fact I never had a clock in my workroom
– Thomas Edison
So I feel even more like I'm onto something. And at least if someone thinks it's weird, I can say, "Well, it worked for Edison". I recommend you give it a try and see for yourself, especially if you're a bit bored with your job.
Of course, sometimes you need to know the time. Even if you don't care about it, there are still meetings, appointments, plans, and schedules. To that end, I wrote a little clock app a while ago and use all the time. I've released it in case someone else might find some use of it. It's called Clock and it's a clock. Really. It just overlays the current time on the screen and is meant to be opened with Alfred (or QuickSilver or Launchbar or whatever). It's super lightweight, so I can open it instantly, check the time, and then close it.
But, your mileage may vary. Please don't blame me if you lose friends and alienate people because you keep missing all your meetings and appointments.