2 portals · 26 items held back · Valheim 1.0.17
Portals
A Portal won't let you through carrying any of 26 items — 11 ores and scraps, the metals made from them, and a few more. The Portal – Stone lets everything through. Only players travel: carts, boats and tamed animals can't.
Items that can't go through
Carrying any one of these, the portal answers “An item prevents you from teleporting”.
The portals
26 items held back
“Connects to another portal with equal or no tag.”
Build:
10× Greydwarf Eye
20× Finewood
2× Surtling Core
Near: 
Workbench
Every item goes through
“The powerful energy source lets you pass through even with the most valuable of items.”
Build:10× Greydwarf Eye
30× Grausten
2× Molten Core
Near: 
Stonecutter
World modifier
Portal Items
Every item goes through portals, ores and metals too
Normal
The game's default: the rules above.
No boss portals
Portals don't work while a boss is active, and dungeon doors won't let you out of an active boss dungeon
No portals
Portals don't teleport ("Blocked")
Set when making the world, or later by the host with setworldmodifier portals <option> — see world modifiers.
Questions
›What items can't go through portals in Valheim?
26 items: Black Metal, Black Metal Scrap, Bloodgold, Bronze, Charred Cogwheel, Copper, Copper Ore, Copper Scrap, Dragon Egg, Dvergr Extractor, Flametal, Flametal Ore, Hildir's Brass Chest, Hildir's Bronze Chest, Hildir's Silver Chest, Iron, Iron Ore, Iron Pit, Mechanical Spring, Petrified Tissue, Scrap Bronze, Scrap Iron, Silver, Silver Ore, Tin, Tin Ore.
›Can you teleport ore in Valheim?
Not through a Portal. The Portal – Stone lets every item through (“The powerful energy source lets you pass through even with the most valuable of items.”), and the world modifier Portal Items does the same for every portal.
›Can tamed animals, carts or boats go through a portal?
No. A portal teleports only a player who steps into it (TeleportWorld.OnTriggerEnter takes the Player); carts, ships and tamed creatures stay behind.
›How do portals connect?
By tag: “Connects to another portal with equal or no tag.” Each portal holds a single connection, so a tag links two portals.
›Why does my portal say it is blocked?
Portals don't teleport ("Blocked"), with the No portals world modifier. With No boss portals: portals don't work while a boss is active, and dungeon doors won't let you out of an active boss dungeon.
Formula
A player goes through if the world has no portal block, and every item they carry is teleportable — or the portal allows all items, or the world has teleportall set.
The Portal – Stone can be built from the Ashlands on (the site's tier for its piece).
TeleportWorld.Teleport, Inventory.IsTeleportable, item teleportable flags and TeleportWorld.m_allowAllItems from the game files — Valheim 1.0.17