When hydrochloric acid reacts with sodium hydroxide to produce sodium chloride and water, is that a double displacement reaction?
Yes it is, it can be helpful to think of water as hydrogen hydroxide to see why this is true.
HCl + NaOH -> NaCl + HOH
Double diplacement reactions are summarized as follows:
AB + CD -> AD + CB
H = A
Cl = B
Na = C
OH = D
Water is HOH or AD
Here is a video to help out with other acid-base reactions.