Basically you have two ways of easily collecting text to the same file.
Use a scripting program like AutoHotkey
In order to collect text, I started out with a simple AutoHotkey script. AutoHotkey is an amazing tool. Just put a bit of effort in learning the basics and you will be able to make your computer work a lot easier. The main point of using AutoHotkey for most users is creating hotkeys for common tasks. Here's an example for a hotkey that will copy the selected text and paste it at the end of the file mynotes.txt without opening it.
^+c:: ; Control-Shift-C as a hotkey
Sendinput ^c ; copy selection, mimicks control-c
Sleep 1000 ; wait 1 second until clipboard is full, use at least 300
FileAppend, `n`n%clipboard%, C:\folder\mynotes.txt ; Add clipboard content to the end of a text file. Insert 2 new lines before inserting the clipboard with `n`n
This works very reliably. Save the code above in an ahk file and place it in your startup folder. This way it will run when you boot your computer. Realize that you have to change the file path from C:\folder\mynotes.txt to the path where you will want to save your file. Vary the file path according to your own needs.
If need be, you can expand the AutoHotkey script to include a time stamp and/or the website the text was copied from (making it similar to Evernote). If you want to know how to do that, I suggest you read up on AutoHotkey basics
For would-be users of AutoHotkey I recommend reading this tutorial over at eHow: http://www.ehow.com/how_8506399_can-keyboard-do-repeatable-tasks.html
Use a ready made app like ClipTrap
And one more thing: I've just remembered a small freeware tool that does something very similar. It's called ClipTrap and it is for Windows: http://skwire.dcmembers.com/fp/?page=cliptrap. There are no configuration options, though. And it does not save any formatting (like HTML or RTF), though the AutoHotkey script does not either.