Neither have I.

Never have I ever ridden on an elephant.

I have!

Never have I ever been married.

Neither have I! That's a long ways off yet. [lol]

Never have I ever pulled an all-nighter (without going to sleep in the "morning." I've seen the sun came up, but then I went to bed. [:P])

I have. More than I could count. [yes]

Never have I ever watched Cirque du Soleil live.

I have, but only because I wasn't using it at the time [ninja]

Never have I ever been to the hospital (as a patient)

I have, I went to the ER one time when I was a kid. I tripped in a grocery store and cracked my head open on a shelf...and the employees freaked out. >.>

Never have I ever climbed out of a bedroom window.

Ouch! I have I think. I know I've climbed in through my kitchen window when we were locked out.

Never have I ever eaten sushi

Neither have I (not seriously anyways)

Never have I ever fed a giraffe

Neither have I

Never have I ever seen the statue of liberty

I have, but only from a distance. Never been up in her hair, or whatev. :)

Never have I ever been to Buckingham Palace.

Neither have I, but I would like to. (I also want to see the Statue of Liberty. Was it cool?)

Never have I ever been outside the USA

I'm a navy brat, but we stayed on base when he went out of the country XD
Neither have I, but I've been bullied (viciously by my younger brother when we were kids)

Never have I ever been scuba diving

Neither have I [lol] I'd like to go though

Never have I ever been mountain climbing

I have, I don't think I have in years.

Never have I ever swam in a lake.

Neither have I (that I can think of)

Never have I ever run a marathon

I have.
Have not.
fireprincess beat me to it, lol xD

Never have I ever been on a zipline.

Neither have I.
Good one. xD

Never have I ever been on a cruise.