Cut, cut, cut!
No, I'm joking. Whether you cut the spikes or not is entirely up to you and all about personal preferences. I'm a cutter. BUT, if you leave the spikes on, they might continue to flower in a while, shooting new buds from the green growth tips at the end, or maybe branch out from the nodes on the spike. I think a live phal spike can go on for ages doing this.
When I say cut, it's because I personally prefer to give the plant a bit of a rest to focus on leaves and roots before it begin growing a brand new spike. I just like the appearance of new spikes more than these (often) lanky, long old spikes. But it's entirely up to you what you want to do.