Apple - OS X: View Zip File as Folder

If you're comfortable with the command line and just want to get a list of the files inside the zip file, you could also use the zipinfo command:

$ zipinfo
Zip file size: 465 bytes, number of entries: 3
-rw-r--r--  2.1 unx        6 bX defN 18-Jun-19 05:00 baz.txt
-rw-r--r--  2.1 unx        6 bX defN 18-Jun-19 05:00 foo.txt
-rw-r--r--  2.1 unx       23 bX defN 18-Jun-19 05:00 bar.txt
3 files, 35 bytes uncompressed, 41 bytes compressed:  -17.1%

Or, unzip -l:

$ unzip -l
  Length      Date    Time    Name
---------  ---------- -----   ----
        6  06-19-2018 05:00   baz.txt
        6  06-19-2018 05:00   foo.txt
       23  06-19-2018 05:00   bar.txt
---------                     -------
       35                     3 files

Edit 2019
Zipster is dead & gone, see other answers below.

Zipster does exactly that.

blurb straight from their site

What is Zipster?

Ever been envious of the way Windows users can just browse into Zip files, copy files in and out of them with ease and all without running a Zip utility? With Zipster, your Zip files are just like another folder in Finder. Plus, unlike on Windows, you can open files and save into them from any application.

Zipster is

  • Free.
  • Fast. Writes and compression are done in the background so you can get on with your work. And we’ve done a bit of work to make reading snappy too.
  • Friendly. No more pesky .DS_Store files — and your friends on other platforms won’t be complaining any more.
  • Useful. In addition to plain Zip files, Zipster works with JAR, WAR, ipa and apk files.

It does have slight limitations when it comes to trying to put things away; it reacts a bit like a mounted .dmg except it's right where the file was, not on the desktop, but it's not a bad attempt at transforming .zips into folders.

Here's one that people often overlook: BetterZipQL. This is a free module for Finder's "QuickLook" function and allows its Preview pane to show you the contents of an archive just as if it were a folder full o' files.