Oh, there were a lot of incidents were the election was close or disputed. Here are two of them, both from the Middle Ages, because that's the era I'm most interested in.

Philipp of Hohenstaufen vs. Otto of Brunswick Philipp and Otto were members of rival families (Hohenstaufen and Welf) that were related in numerous ways, but still hated each other due to their contest for influence in the HRE. When the Investiture Controversy arose, the Hohenstaufens chose the Ghibbeline (pro-Emperor) and the Welfs chose the Guelph (pro-papal side) so thoroughly that their gave the name Guelph derives from their name.

After HRE Heinrich VI died in 1197, his heir, Friedrich, was still a baby and no one was wild about the thought of electing a baby emperor, so Philipp (one of Heinrich VI's brothers) became the Ghibbeline candidate instead. The vote was then split between Philipp and Otto and neither was willing to back down and devoted themselves to bribing electors to try to win the support they needed.

In the end, Otto blinked first, but then Philipp was assassinated in 1208 by a Wittelsbach for unclear reasons. Otto then became emperor and annoyed everyone until he was eventually excommunicated and forced to resign in favor of Friedrich II, the now grown son of the late HRE Heinrich VI. He then ordered a group of abbotts to beat him the death. (For whatever reason, all but one of the five surviving sons of Friedrich Barbarossa and four surviving sons of Heinrich the Lion died before the age of 35, violently, or both. The lucky survivor was Otto's older brother, Heinrich the Elder, who outlived them all and died peacefully in his bed in 1227, aged about 54-55.)

Alfonso X of Castile vs. Richard of Cornwall After the aforementioned HRE Friedrich II died in 1250, there was no emperor for many years because the papacy had decided it was sick of the Hohenstaufens and wanted them gone. In between then, though, Alfonso and Richard both wanted to be elected king of the Romans in 1257 and fought over the results.

Alfonso, in addition to being king of Castile, was also the son of Elisabeth of Swabia, one of the daughters of Philipp of Hohenstaufen. Richard was the second son of John I of England and Isabelle of Angoulême and thus the younger brother of Henry III. His only real connections to Germany were that his sister, Isabella, had been one of the wives of Friedrich II and his great-aunt, Matilda, was the wife of Heinrich the Lion and mother of HRE Otto IV.

Alfonso's attempts to win over support fell flat. He irritated the papacy due to his connections and alliances with the Ghibbelines and never even traveled to Germany. Richard did go to Germany briefly and was crowned king of the Romans, but then had to return to England when his older brother begun seriously clashing with his barons.

Other disputed elections include HRE Ludwig IV vs. Friedrich the Fair of Habsburg and François I of France vs. HRE Karl V and many, many more. If you want more examples, wikipedia has a long list of the numerous anti-kings that existed throughout the history of the HRE.