New lifters should always be installed. Reusing worn lifters on a new cam is asking for trouble. With flat tappet cams, lobes are ground with a slight taper so they will spin the lifters as they push them open. The lifters are also slightly convex on the bottom to reduce the point of contact and to promote rotation. If lifters are worn flat or concave, the mismatch between lobes and lifters will accelerate wear and probably ruin the new cam in short order.
New valve springs are also recommended in many instances, especially if the cam is a performance grind with increased lift and duration.
Pushrods should be checked for straightness and replaced if any are bent. Rocker arms should also be inspected and replaced if found to be worn or damaged.
Other parts that might be needed include a cam drive gear and chain set (or belt on overhead cam applications), a timing cover gasket set, and assembly lube (to prevent lobe wear during cam break-in).