Destroy it, over the long term. One of the drawbacks of growing any climber up a wooden fence is the inability to repaint/retreat with wood paint/preservative once the climber's covered it. Ivy also roots into wood, and will increase in size, so unless its a very strong, expensive fence panel (in which case it will cope for longer), it will eventually bring it down simply by its weight. In some gardens though, the only thing keeping the fencing in place is incredibly overgrown ivy, I've come across that more than once, and when you cut the ivy back, the fence is completely rotten beneath.

I put in a new close-boarded fence 18 months ago and already ivy from next door is creeping between the boards and if left the thickening stems will eventually ruin the fence. The neighbours were so delighted with the fence, and of course, they have the smart side, yet are allowing this to happen. I will have to approach them this week about it. Your query has served to remind me!
At the bottom of the garden is another fence exactly as Bamboo describes. It is not mine, and my deeds prove it, but the people there say it is not theirs either! I keep the ivy trimmed on my side but the other side is very overgrown and if they removed the growth the fence would certainly collapse as it is totally rotten.
So yes! Remove the ivy while you can! Put up some wires and grow something non clinging. Wires can be fixed in such a way that the whole climber can be laid down while you treat the fence.