I've worked out a system to cope with it.
STEP 1 - Compartmentalize Accounts
I have two businesses that are totally separate, so each has it's own email. Then I have a personal email addy. I use Gmail for two of them, so spam filters there do a lot of work once you set them up well.
The third email is on a biz domain name and is the oldest of the addresses (my RE brokerage), and it gets notably more spam. Partially that's attributable to various assistants that used to sit at my PC in years past. That one requires a bit more weeding.
STEP 2 - Make it easy to get to
Checking three accounts is a pain in the rear if they're on totally separate interfaces. Dowlnoad Mozilla Thunderbird to the computer and set up separate accounts on it for each email you need it to download. Gmail will let you download it as a Pop3. You now have all the accounts on one interface. You can look at each separately, or look at the overall inbox for all of them.
If you have several accounts that do not need to be separate, point them all at one account on thunderbird. Name your accounts in a way that you immediately know which is what.
STEP 3 - Create Folders and USE THEM
You can create folders for storing away emails in Tbird so they are not cluttering the inbox. Dont make it complicated or large... paint with broad strokes. Set up a folder for family, for correspondence from various organizations or groups you're in, for feedback on a blog or something, for password related emails, for technical reference, etc.
Rather than getting rid of stuff like the accounts at Shoemoney or subscriptions to techie newsletters and such... set them up their own folder and set the filter to deposit them there on arrival. They won't clutter the inbox, but will be there when you want to browse them, neatly sorted by date.
HOW to pick Folders? (and set up filters)
While your box is overcrowded... before trying to clean it... sort it by sender. You'll be able to see at a glance what folders you'll need. It will also make getting rid of the spam a snap, and tells you which filters you need to set up. Set the folders up, then while they're sorted by sender, drag and drop 'em as a group.
Gmail allows easy access from wherever I am, but normally I'm on my own laptop. I can still check gmail accounts if I'm away, but having it all converge on my hard-drive via Thunderbird makes it easy to manage and maintain. It allows me to color code emails in different colors for different needs.
They say there's 3 different learning styles...
There's the guy that learns by reading what others have done, the guy that learns by watching others... and the third guy that just has to pee on the electric fence to see for himself.
The setup I use is the result of having done it every wrong way possible in the past. I've used email since they invented it, and trial and error led me to this setup. Give it a shot... beats the heck outta making the same mistakes yourself.