A Fistful of Dollars is Pride. Ramon has been very boastful about his skills with the rifle and Joe challenges him to see if he really is better than a man with a pistol.
For a Few Dollars More is Wrath. Mortimer wants El Indio dead for what he (Indio) did to Mortimer's sister (raped her until she committed suicide).
The Good, The Bad and The Ugly is Greed. All three of the main characters want the gold. Cue plenty of Chronic Backstabbing Disorder from all three.
Or, at least Joe and Manco are (Blondie doesn't really fit into it, being from at least a decade, if not two, earlier). Underneath the poncho, they dress rather similarly and use the same snake handled pistol. Something happens that Rowdy is no longer trail boss, perhaps wiped out by the Rojos.