Hi Smokey...welcome to Orchidboard
There are two different thoughts on the subject, it's up to you in the end.
Some folks leave the spike, hoping for another bloom or two. It is certainly possible for this to happen. If you see the spike turning brown, you can assume that's not going to happen and cut it down. If additional blooms do pop up, they are usually not the same quality as the first were.
Other folks (like me) prefer to cut the spikes, allowing the plant to put it's energy into becoming a stronger plant so that the next round of blooms will be just as fabulous (or more) as the last ones.
Decisions, decisions...
Do you have any other 'chids?