What is the advantage of an optical viewfinder over an electronic viewfinder?

Optical:

1. Full color gamut, resolution, and dynamic range of the eye
2. Coarse manual focus is still faster with OVF.
   
3. You can upgrade to split prism focus screen
4. Doesn't use battery. Both extends battery life, and usable with camera turned off.
   
5. Instant. No lag. This was a severe problem with EVFs. Modern EVFs can be very fast, although they get worse in low light

Electronic

1. You see white balance, gamut limitations of the sensor, etc. before you shoot.
2. You see exposure before you shoot. Beginners can do full manual from day one.
   
3. Focus zoom makes for hyperaccurate manual focus (and better use of autofocus)
4. Camera sees what it is shooting -- smarter automatic modes.
   
5. No moving mirror. Less camera shake for sharper photos.
   
6. You can review photos accurately.
7. Potentially more on-screen information. Sadly, this is more theory than practice. Higher-end OVF cameras (D700, D3, etc.) start to add all the fancy electronic levels, etc. you see in EVF cameras. You just get them in somewhat lower-end EVF models. EVF models don't have fancy zones, etc. 
8. Much bigger image relative to entry-to-mid-level dSLRs.
   

Switching from OVF to EVF is initially a bit painful if you're used to OVF. It took a while before I got used to losing the zen/connection to reality of OVF. Now that I got used to EVF, I have a hard time going back.

Not all EVFs are the same. Many of the cheaper, small sensor cameras have very poor, laggy EVFs. At the same time, not all OVFs are the same. Many full frame cameras have very large, very usable OVFs. I hate using APS dSLRs, now that I've used EVF, but a 5D Mark II is decently usable.