How do I find traders to buy the loot I collect in Skyrim?

I have a lot of valuable loot that I collect in Skyrim. I have no need for most of it, and would like to sell it off, but it's hard to find a merchant that will buy all the random loot I've collected. How do I find a trader that will buy all my valuable loot?

In most cities, there's a number of merchants who will buy various different wares from you which are comparable in kind to the ones they sell. And most cities and towns have at least one "general goods" merchant who will pretty much buy anything. In Whiterun, you'll want to visit Belethor's General Goods.

For stolen merchandise, you'll need to find a fence. The earliest one you'll probably have access to is Tonilia, in the Ragged Flagon under Riften.

The main limitation you'll run into here is that most merchants only keep 500-750 gp on hand, and fences start at around 1k. So, if you empty their bank by selling too much to them, you'll need to wait a couple days before they have the funds to buy more from you. There's a few perks and other workarounds that can be used to deal with this.

Also, be aware that most stores are only open from 0800-2000. If you're trying to sell your wares at night or early morning, you'll probably have to wait.

I strongly recommend you search this site for other skyrim questions on this topic, as I'm sure there's at least one or two that will address all your merchant-related inquiries.

Related:

Is it possible to sell stolen items?
How often do merchants replenish their gold supply?
What merchant has the most gold?

All of the perks that will help you sell stuff easier and to more people are in the Speechcraft skill tree. The ones you'll particularly be interested in are:

Merchant - Sell anything non-stolen to any merchant.
Investor - Give 500 gp to a merchant to permanently increase their bank by 500 gp.
Fence - Sell stolen goods to any merchant you've invested in.
Master Trader - All merchants have 1000 additional gp on-hand.

These are all on the left side of the tree, with Haggling and Allure as pre-requisites.

If you want to sell big-ticket items (items over 1000 gold) and you want to be able to sell your stuff without having to worry whether or not you killed Belethor, you need to improve your speechcraft to 100.

There's a quick way to level up Speechcraft:

1. Go to the Black-Briar Meadery in Riften.
2. Talk to Ungrien.
3. Ask him about Maven Black-Briar.
4. Ask him what he really thinks (appears as an option after you hit 25 speech)
5. Rinse, lather, repeat.

Once you do that, you should accumulate and spend skill perks on the Speechcraft tree (the 'left' side), and you'll be able to do the following things:

1. Traders accept items of all types (weapons, apparel, potions, ingredients, misc, books).
2. Better prices from people of the opposite sex.
3. Invest in any business, giving them 500 extra gold to trade with all the time.
4. Fence any stolen item at any trader you've invested in.
5. Every trader you've invested in has 1000 extra gold to barter with.