Well, 4 Zeppelins were shot down during the Battle of Verdun but I believe they were all lost to AA fire.

I can add to this the somewhat famous takedown of LZ37 by Lt. Rex Warneford who, when bombing a zeppelin yard, saw a zeppelin returning from a bombing raid and attempted to shoot it down...with his carbine. The Zeppelins machine guns drove him off and LZ37 wisely decided to use her superior climbing ability to get away....not aware that Warneford decided to climb and follow her FOR TWO HOURS until she decided to land at which point he dropped his bombs on her roof. The explosion almost destroyed Warnefords plane as well, but this was the first Zeppelin ever taken down by aircraft. (1915)

If I recall correctly, 1916 was the year the British started to deploy incendiary bullets, which have a tendency to make giant bags of gas burn. It was this year that the first airship was shot down over London (Although if I recall correctly it was a Schutte-Lanz not a Zeppelin so I guess technically we can't add that to the tally, but two navy Zepplins were shot down within a couple of weeks of it, one by AA and one by aircraft.)

There may be a few I am forgetting here in the middle, again sorry, I don't have my sources handy as I am on mobile at the moment.

In late 1917 (October or Novemeber, I forget which) there was a surprise raid of ELEVEN Zeppelins that took the English totally off guard, but on the return to the mainland allied fighters took down five or six (again, sorry for being fuzzy) of the airships.

The last big raid I am confident about was in in 1918 because Strasser himself lead the excursion. He lead five height-climbers to England and was shot down by a DH4 at over 20000ft. The other four Zeppelins cut and ran.

This is an incomplete list, of course, it is only the more notable losses that I am absolutely confident about without my sources. I know that around half of the 115 Zeppelins ever made were lost (not all shot down, of course, there were incidences like the explosions at Ahlhorn that have never been explained) and crew loss rates were between 35-40%.

I hope someone can come in and expand on this for me, or at least source some of it until I can get home in the next few days (I believe all of this information is available in Wilbur Crosse's "Zeppelins of World War I" and some should also be in Gerry White's "Zeppelin Nights: London in the First World War" although that publishing focuses more on...well...London.)