Oo, it's terrifying to have a big pile of papers. There could be anything in there. Unpaid bills, your diploma, letters from an ex, uncashed checks. Anything!
But probably it's almost entirely not that kind of stuff. I'm betting it's mostly four things:
3. Stuff to shred
4. Manuals and receipts for the purchase with which they came
There are probably some other big categories that are well-represented. For example, packing slips or receipts that came with things you bought. You also may have papers relating to your health: bills and insurance statements from doctor visits, those information sheets that come with prescriptions, etc.
There are two main ways to conquer random stacks of paper: targeted missions and steady chipping. Targeted missions are great for feeling a big positive impact fast. Decisions can be tiring, so rather than picking up each piece of paper and deciding its fate, make one decision that can apply to a whole lot of pieces of paper.
An ideal decision to start with is, "All the catalogs in the house can be recycled. While I'm conquering having too much stuff, I'm not buying more stuff, and they'll be sending me another catalog in the future anyhow, so goodbye to all of these." Similar is the decision, "I want to catch up with my other papers before I add more, so all magazines and newspapers before the current issue can be recycled." Either (or both) of these decisions allow you to attack a stack without having to do a lot more thinking. All you're asking is if it's one of those things you said you're going to recycle. Yes and it goes in the bin. No and it stays in the stack. That simple.
Do that one targeted mission against the stack and then stop. Give yourself credit for forward progress and go do something you enjoy. Flinging yourself against the paper wall until you collapse isn't the road to success; define your current lap, run it, and then take a rest and your reward.
Perhaps in the course of doing that targeted mission you'll notice some other easy target. For example, you might see a lot of health-related items. Your next targeted mission can be to pull those all out of this stack and consolidate them in a folder or box which contains only health materials. That transforms a mystery blob into a clear category. If you're later looking for your passport, you know you don't have to look in there because it's not a health-related item. Categorized chunks are easier to navigate than random stacks.
After the obvious targeted missions have been run, the way to purge the rest of that amorphous blob of paper is to chip away at it steadily. Working just 5 or 10 minutes at a time—with a timer!—is all it takes. Don't get hung up with taking action on any individual item. Merely spend those 5 or 10 minutes quickly identifying each successive item you pick up and then throwing it away, recycling it, shredding it, or putting it in a labeled folder based on a category (e.g., charitable donations; letters from Mom) or an action to be taken (e.g., add to address book; scan and then discard the paper; add to calendar)
The folder can go in your inbox or even in a stack of "to be dealt with" folders, so long as you have the sacrosanct rule that nothing goes into a folder that doesn't belong in that folder's category. Remember: A set of categorized chunks is progress over a random mystery pile!
The key to making chipping away work is to keep it steady. Do another 5 or 10 minutes every day. It's quick, you'll make it through those minutes!
If you run into a occasional difficult item that you just don't know what to do with, something that hinders your progress, put it on the bottom of the stack and return to it later. Take your easy wins first and then use that victory to give you strength to tackle the tougher stuff.
As you go, keep an eye out for useful patterns to save yourself from having to repeat this chore. If you had to throw a lot of the same catalogs or unread issues of a magazine into the recycling bin, get off that mailing list or cancel that subscription; it's costing you more time, space, and pleasure than it is giving you. If you have a lot of receipts you held onto in case you needed to return something, start a folder for those and keep them all together, where it's easy to purge the oldest ones on a regular basis. Optimize your inflows for quality over quantity and ease of use.
Paper piles can be beaten! Chime in in the comments to tell of your epic battles and how you won out against your stacks.