The application(s) you want are built into the Mac OS -- they are called "Finder" and "Spotlight Search". Learn how to use the built-in features and directory structure of your Mac and you will simply not need to resort to 3rd party applications. Put simply, if you can't organize or find your files on your Mac then you either need to invest some time in learning how to use the OS or you are "doing it wrong".
In managing Macs and PCs for thousands of people over my career I have seen this over and over. Users that refuse to organize their documents when saving them then want some magical software solution that can read their minds and find anything instantly. Unfortunately, both Apple (Finder "All My Files"), and Microsoft (Explorer "Libraries") have attempted to cater to these users but have instead just perpetuated the issue. I can't tell you how many times I've asked someone where they saved a file and received an answer of "on my hard drive".
To instantly elevate your status as a Mac power user you simply need to learn the [command]-[spacebar] shortcut to using Spotlight to instantly find or launch anything on your Mac in a few keystrokes.
I beg to differ.
I am in academia, and have always been meticulous with storing my data. Nested folders, naming regime, tagging. Yes, Finder/Spotlight does a fine job of locating individual files, or several that meet a range of criteria >> IF you know what you are looking for...
By that I mean, all the nested folders and proper storage methodology in the world is still limiting when you are faced with 2000/5000/10000 documents. It's like walking into a public library, without really knowing what you want, only that you want to find something interesting. Or sitting down at your computer with the Google search bar open before you yes, you can find anything, but what to look for?
The above is not directly related to what you were saying yes, Finder/Spotlight can locate the file, just like the library catalogue will. But where Finder/Spotlight fall flat, and where any decent document/information manager will excel, is placing you, the user, in
control of that library.
I needed something like Devonthink to finally give me access to my information. It was always there, I could always find what I thought I needed, but I didn't have true access. The moment you cross the threshold of a couple hundred documents, your ability to 'control' that library diminishes exponentially. That is where a document manager becomes essential. It unlocks all that information, and provides access to it in any which way you need it and often times, in ways you never realised you needed.
No doubt any Mac Power User can use Finder/Spotlight/Alfred/Launchbar/QuickSilver to find stuff. But if you need to manage stuff, and gain control over what exactly that stuff is then Finder/Spotlight is the beginning not the end.
To be clear, if you're simply needing a system to occasionally find where you saved that last utility bill, or funny attachment, or work Report then yes, applying sensible storage mechanics in conjunction with Spotlight/Finder (and OSX tags) will be more than sufficient. Anything more rigorous than that, and I'd reason you need to careful that you don't end up limiting what is possible, simply by virtue of not appreciating what is possible.