Does FedEx keep track of one's flight hours? I've looked around VIPS and couldn't find anything.

I was thinking about keeping a personal logbook, but on the other hand, I've made it this far in my career without one...

Aramp,
Go to Crew Information->Operating Experience Summary
It's all broken down for you. I use it every time I fill out my Flt Physical Application.

Resources tab
Reports
Pilot Block Hour/Landing Report

This will give you the data for each leg not just the summary as referenced above.

Awesome! Thanks gents! Well with all this, no need to start a logbook now.

Well, that's a much better technique than my WAG. I'll have to use this from now on instead of just adding 250 to the last one.

I always ask other pilots loggings flight times in their logbooks if they're logging time to get a real airline job!*?

250?
I usually just add 300!!