You can keep these things (as long as you log into your characters):
Characters made on a premium account have a limit of five gold max and have their last two inventory bags locked. The gold cap is removed and the forth and fifth bags are unlocked if you have logged into this character while you have VIP status. (Basically, if you ever want to play other characters and not have a gold cap or limited to 3 inventory bags, just make a bunch of characters on different servers and log into them before you let your paid time lapse).
Extra Trait slots are treated just like gold and bags. Premium players have a limit of 1 or 2 (depending on type) trait slots available. VIP players have all of them. Just like gold and bags, this is kept if you log into a character before you downgrade (even if the trait slot hasn't been unlocked yet).
You keep the ability to swift travel on characters you have logged into during VIP status (as long as you meet the requirements for that location).
You will go from being able to post 30 items on the auction house at a time to only 5 items.
Characters that have earned their riding skill while having VIP status keep the privilege. Premium players must buy their riding skill from the store. So if you have several 20+ level characters, make sure you get the riding skill on each before you downgrade.
You will keep anything you purchased from the store during your VIP status, even if they are VIP only items. Expansions, Adventurer's Pack etc.
You will lose these:
- You will no longer get 500 Turbine Points a month
- You lose access to customer service (GM support tickets)
- You will fall back to a high priority for the login queue (Behind VIPs but in front of free2plays)
- You will lose 20 wardrobe slots
- You can no longer spend Destiny Points
- You lose access to Monster Play and the Ettenmoors PvMP (Except for the Reaver class, all other classes will be locked but they will not be deleted if you have them)
- If you haven't yet purchased quest packs your questing will be limited to the starter zones.
- Some instances and deeds (linked to quest packs) will become locked.
- You will not earn any more rest experience (you will keep and be able to use rest experience you have earned before you downgrade).
- Your chat and mail will be more limited (You can only send so many tells or so much mail in a certain timeframe).
- Your crafting will be more limited (You can advance in your current tier, join the crafting guild, and you can gain guild reputation but you will not be able to advance to the next crafting tier).
- Premium accounts only have access to three character slots per server while VIP has five. When you downgrade you will lose two of them. If you have more than three characters created on that server you will be asked to choose three and the other two will be locked until you purchase more character slots. (If you have purchased Mines of Moria physical copy or the expansion from the store you will have an additional 2 character slots available that you will not lose in addition to the Warden and Runekeeper classes)
If you want to read more about the transition or about purchasing expansion packs etc, I suggest you read this post on the official forums. It has a lot of information.