Throughout the entire oeuvre of Shakespeare, Falstaff remains one of the most memorable characters (something Orson Welles took advantage of for his Shakespeare film Chimes at Midnight). In Henry IV, Falstaff is an important figure and companion to Prince Hal and serves to influence the prince in many ways. While the relationship between Hal and Falstaff at times seems simplistically fatherly, the reality of their relationship is complex.

Prince Hal frustrates his father, King Henry, by wasting his time in pubs and taverns with hooligans and other questionable companions. The most charismatic, bumbling, and lively of the bunch is Sir John Falstaff. Throughout the beginning of the play, Hal and Falstaff drink and burn away the time by jesting and thieving; all the while Prince Hal admires Falstaff as a friend, but vows not to become too similar to him.

In one line, Prince Hal jests at Falstaff's infamous heavy-nature, “How now, my sweet creature of bombast! How long is't ago, Jack, since thou saw'st thine own knee?” The two men jest with one another and tease one another. In another passage of the play, Hal, knowing Falstaff's tendency to exaggerate stories, robs and harasses Falstaff and several other friends; later, Hal jokes about Falstaff's false re-telling of the robbery. While Falstaff serves as an outlet for Hal to have fun and be carefree, Hal frequently feels obliged to abandon the low-class Falstaff in favor of his own princely duties.

There is no one relationship between Hal and Falstaff. Rather, there are several.

Falstaff fills the position of surrogate father, and one a lot less scary than Hal's real dad.

Hal and Falstaff are drinking buddies; they enjoy wasting time together.

Falstaff is a way for Hal to get access to not just the lower classes, but the riffraff of society (thieves, prostitutes, etc.). This is both a kind of slumming and a kind of education for the future king.

Finally, Falstaff is a kind of dark mirror. Hal wants to shrug off the burden of honor, but he sees in Falstaff the results.
Greg