Sample Full Build
Poppy is largely a 'stick to the core items' champion. They all tend to do just about everything she needs.
Sunfire Cape helps her trade and push lane.
Ninja Tabi solidifies her defense and mobility.
Iceborn Gauntlet tops up her mana pool, makes her a threat, and helps her lock down targets.
Spirit Visage provides most or all of her needed magic resist, tops up her health pool, and adds to her CDR.
Dead Man's Plate makes her even more survivable, and helps her get those run-down pins.
Guardian Angel allows her to go all-in in late game fights.
That being said, there are several items worth considering in rare cases.
Mercury's Treads crop up on the build list once in a while, in order to help Poppy run through the enemy CC line and disrupt priority targets.
Randuin's Omen is an excellent pick-up against high-crit teams.
Zz'Rot Portal can be used to proxy push or assist in siege.
Warmog's Armor if you need health and siege sustain (rarely useful).
Thornmail if you're the only real focus of heavy auto-attackers.
Banner of Command for CDR and lane pressure.
Locket of the Iron Solari if your team really needs the AoE mitigation.
Banshee's Veil if you have everything and need budget Magic Resist.
Trinity Force instead of Iceborn Gauntlet if you're going for more of a duelist play-styles, and less of a team-fight play-style.
Blade of the Ruined King to really emphasize that duelist play-style. Very uncommon build.