Zombies have jumped for a long, long time now; They just need to be presented the opportunity to.
And they do not register traps as anything more than a block in the world- If you obstruct the path with traps, they will make a path some place else.
EG: Don't build wood/iron spikes 2+ high above ground level, only build them 1 high, or better yet sink them into the ground- They perceive 2 high spikes to be as solid a wall as if it were two normal blocks.
Further, Zombies navigate by block HP and time taken- The path of least overall resistance is the one they will typically take.
Traps of all kinds are viewed as blocks with HP values, just like building blocks- Iron spikes for example have i think 350hp(?) times 5 layers for a total of 1750hp; So a 2 tall 'wall' of iron spikes would not only equivalent to a cobblestone wall, but in fact more durable than a cobblestone wall.. So if you build yourself a square wall of cobblestone blocks(or worse...
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