Thanks, this is great. But it is by no means complete. At least not in my case. It showed only 2 arrivals and 2 departures in 2015 when I have flown to/from the US many more times than that. I would not rely on this for tax purposes (I also need it for this reason).

Edit: Just noticed this in the FAQ:

What information can I obtain from the website?

Answer:
The I-94 website provides you with the most recent I-94 admission record and limited travel history. The most recent I-94 admission record can be printed and used as evidence of a lawful admission. <snip>

'Limited' seems to be the operative word.