The 70-200mm f/2.8L IS II will hold up to the extenders better than any other 70-200mm version, especially to the 2x extender. Unlike Homer, I'm fairly happy with the IQ of the 70-200 II + 2x II extender (although the 100-400mm is just slightly better at 400mm). Personally, I chose the 100-400mm over the 400mm f/5.6L for two main reasons: the 100-400mm has IS (and for static subjects at 400mm, I will often want to shoot at much slower than 1/800 s or so), and the 100-400 is also much shorter for travel because it retracts.

I use the 70-200 II with 2x as a substitute for the 100-400mm when it's raining, or when I'm mainly going to shoot with the 70-200 (e.g. outing with kids) but might want the extra reach without carrying two big white zooms. Are a couple of samples of the combo (click for larger), one on APS-C and the other on FF:


EOS 7D, EF 70-200mm f/2.8L II IS USM + EF 2x II Extender @ 400mm, 1/160 s, f/5.6, ISO 3200


EOS 5D Mark II, EF 70-200mm f/2.8L II IS USM + EF 2x II Extender @ 260mm, 1/250 s, f/5.6, ISO 400