Celibate Hero: Herc actually had three serious relationships during the show, a previous one with Nemesis and a few other serious prospects. Not too shabby, but that's nothing compared to the many women he's turned down.
Sins of Our Fathers: Being Zeus' son, Hercules usually has to deal with anyone with an ax to grind—almost always Hera.
Hercules: That's between you and Zeus. Hera: No, you're what's between us! But if you die a horrible death, maybe he'll think twice next time his eyes start to wander—before he fathers any more half-mortal mongrels like you.
"Well Done, Son!" Guy: He grew up desperately wanting to meet his dad. Even after all the problems and fighting, Herc admits he still has a blind spot when it comes to giving him second chances.
"The reason I didn't tell you about my relationship with my father is just that—there isn't one to talk about. He had the heavens and Earth on his shoulders. He didn't have time to think or care about me."
Ascended Extra: Was meant to be a one-off friend in Amazon Women whose death furthered the plot. However, Michael Hurst so impressed the producers that they changed the ending to leave Iolaus alive. The only reason Iolaus doesn't appear in the next three movies is because they were written before the change was made. Iolaus returned in the fifth movie and was a recurring character in the first two seasons before becoming a regular in Season 3.
Back from the Dead: Died four separate times, but Hercules always found a way to bring him back. These repeated developments became causes for laughter among the crew and even got lampshaded in a few episodes.
Overshadowed by Awesome: A recurring theme in the series. Iolaus is skilled, resourceful, and a kickass fighter. He is not, however, a super-strong demigod, so he sometimes winds up as this. Sometimes he is angry about it ("Pride Comes Before A Brawl" and "The Warrior Princess"), or introspective ("A Star To Guide Them"), or very aware of it ("Medea Culpa"), or it is used to mess with his head ("Redemption").
"Look, I'm no oracle. There are a lot of things I don't understand, but from the first day I met you, I just knew that you were destined for something the rest of us could only dream about! People like me and Jason—normal people, we'll be lucky if our names are even mentioned in the same breath as yours. And that is not always easy to live with."
Composite Character: She's actually a combination of Hercule's first wife Megara (being his first wife, and murdered by Hera however Megara was indirectly killed by her in the myths,where Hera kills Deineira directly in the show)and Deianeira from the myths (the name, and the run in with the centaur)
Demonization: He inadvertently does this to Hercules in "What's In A Name?" He takes his brother's identity to impress a woman, but her warlord step-father starts touting that he has the son of Zeus on his side.
"Well Done, Son!" Guy: In "What's In A Name?", part of his problem is that he thinks Alcmene loves him less just for not being Hercules. He gets over it, though.
Adaptational Heroism: They keep his leaving Medea for another woman, but the implication is that he had a formal divorce and didn't do so lightly. He is also devastated by what happened to his children (with dialogue implying he witnessed it) and trying to make up for what has happened.
The Alcoholic: In his first appearance. He gets over it and is never seen drinking again.
Continuity Snarl: Started off as the king of Argos and a contemporary of Amphitryon (Alcmene's first husband). In his next appearance, he was the king of Corinth. In Season 4, he was retconned into only being a couple of years older than Hercules.
Heroic BSOD: In his first appearance, he's a broken man following Medea murdering their children.
Foil: Contrary to the distant and aloof image of philandering Zeus, Odin is shown to be more involved in the lives of both his family and the mortals under his care. He cares for all theme, dislikes abuses of power, and has a good relationship with his wife.
The Gods Must Be Lazy: He truly cares for humanity, but he rarely interferes with the other Olympians that cause trouble.
The Artifact: She becomes less prominent of an antagonist midway through season 3 in favor of Ares, and doesn't even appear in season 5 or 6 until Back for the Finale yet the opening narration continues to treat as the Big Bad of the entire series.
The Faceless: She initially appeared as a pair of eyes in the sky and usually with a voice. In "Reunions," she finally appears in human form.
Kill the God: He wiped out the Sumerian gods as part of a plan to enter the world. He also schemed to bring about Ragnarök and wipe out the Norse gods. The Olympians were so terrified of him that they fled before he made his way to Greece.
Nice Job Fixing It, Villain: He waged a devastating conflict against the Titans to seize control of Earth. He lost and was banished, but the conflict was so debilitating that the Olympians were able to rise up and overthrow the Titans shortly afterward.
Sealed Evil in a Can: He was banished to another realm by the Titans. A number of plots here and earlier on Xena were to find a way to free himself.
Shapeshifter Guilt Trip: When he meets Iolaus, he takes the form of his father, then Nebula and finally Hercules. He then proceeds to wear Iolaus down with guilt and regret to make him agree to a Deal with the Devil.
Thanatos Gambit: His ultimate plan is to have Hercules kill him while possessing Iolaus. This would send him back into his realm, but also condemn Iolaus to the same fate. Having the Big Good do this would shatter an already weakened balance between good and evil, plunging the world into chaos. (Whether Dahak would be outright dead or just come back was never made clear.)
Villain with Good Publicity: His worldwide cult is full of people who think he's what's best for the world. During Season 5, he pretends to be Iolaus and claims to have taken ambrosia to ward off an insane, god-hunting Hercules. By the time Hercules makes it back to Greece, the "god of light" has many willing followers.
Xanatos Gambit: As he explains to Hercules, all he needed was the sacrifice of a warrior heart to enter the world. He would've settled for Nebula, but Iolaus worked out just fine.
He wants his Thanatos Gambit to succeed, but if Hercules doesn't play along, Dahak will just "take the whole world soul by soul."
Kavorka Man: Just ask the 50 Daughters of King Thespius
Large Ham: Being a fairly campy show, most of the characters fit the bill now and then, but Salmoneus runs on this trope.
The Load: He can't fight, so the best he can do is offer moral support. In "Unchained Heart" he actually freezes up during a crisis, though he feels very bad about it. The few times he's forced into combat (like in "Outcast") have him relying on trickery and potshots.
Hercules: Before we met, you saw yourself as a jester, so that's what you were. I saw you as a hero who didn't know it yet. Once you saw yourself that way, too; well, that's what you became. We are who we perceive ourselves to be.
I Want My Beloved to Be Happy: She walks out on Hercules because an oracle told her that while he would honor their marriage vows no matter what, Greece would suffer without him and that thought would continuously torment him.