Technology has tried – and failed – to eliminate the memo pad in favor of the "paperless environment". But the plain fact of the matter is that note-taking is the most efficient way to quickly (and cheaply) "store" information for later retrieval.
Small side note: Any IT person will state without hesitation that it’s a fool’s errand trying to get the office paperless. People are married to their printers and Post-It Notes in places like that. That hasn’t changed in decades and shows no sign of changing any time soon.
One more note: Never stick a Post-It Note on the computer guy’s monitor where you work, else it will get "filed" (i.e. thrown away and never read). 
Aside from the office place, if you plan to go into business for yourself (or even if you are already), my honest advice is to start getting used to taking notes by using a classic memo pad.
What is a classic memo pad (or memo book)?
A classic memo pad is a top-bound, college ruled book with 75 sheets (sometimes 80) measuring 3×5 inches.
Where to find them?
Office stores. Staples, Office Depot, OfficeMax, etc.
Sometimes you’ll find them at pharmacies like CVS and Walgreen’s. And if you’re lucky your local "dollar" store will carry them also.
Reasons why memo pads will always be necessary
Physically writing something down increases the likelihood of you remembering what you wrote
While typing on a computer is certainly faster it’s not necessarily better as far as memory retention is concerned. Have you ever typed an e-mail to someone, sent it and completely forgot what you just sent immediately afterwards? It does happen – but not with traditional note-taking.
Thumbing thru your notes is easier than trying to make sense of a ton of e-mail
E-Mail, while great, can turn into a mess quickly. For example, if you’ve ever had a really long threaded conversation (with so many re:’s it’s ridiculous), the original intent of the mail is lost in the stack. Digital stack, that is. With notes the only things written down are what matters without the fluff.
Putting your shopping list on a PDA or smartphone is still stupid
The sheer amount of effort it takes to put a shopping list in a PDA or smartphone is absolutely dumb compared to just physically writing a to-do or pick-up list. Doing it the PDA/smartphone way doesn’t even save you any time and furthermore it burns battery life.
Writing notes is the best and fastest way to capture right-now ideas
When you get sudden inspiration you need to capture it immediately. Most of us don’t carry around a dictation device and the PDA/smartphone way is just too slow. The plain ol’ memo pad on the other hand is right there and at the ready.
Why is it even necessary to have an article like this on a tech site?
People in tech want right-now technology. To date, nothing has proven to be faster than writing something down when you need to remember something for later.
With an iPhone the on-screen keyboard is maddening to use.
With an alternative smartphone the tiny keys are also maddening to use.
PDA tech with handwriting recognition is decent but still a bit slow on the draw (literally).
. . .
You could be the next person to have that killer idea for the internet that will change the game of the way things are played.
But you’ll never get that idea down fast enough using tech. Even the super-geniuses of today’s internet, be they businesspeople, programmers or whatever they are all take notes.
If you’re not writing notes, you should start.
Want a paperless Environment ?
Give everyone a manual typewriter!
Have Smith-Corona will travel (or not).
All your points are are great. There is one other quick memo service I have found useful and I use it all the time. Jott.com does have a scaled back free service called Jott Express. I call the Jott number and say either “reminder” for a text message to be sent to my cell phone at the appointed time, or you can say “note” or even “Twitter” and it will be posted on Twitter. Jott did come out of beta and charges for voice to text cell phone or email messages. I have no connection with Jott in any way shape or form. At times when writing a note is difficult such as while driving the service is very convenient.
I’ve been reading articles on this site for a little over two years now and many of them have been pretty informative. However this article… what the hell? This is just plain backwards. Everything you’re written for your reasoning is pretty poor, to be honest.
I’ll agree on the note that when you write something down, you’ll remember it easier. Which is good when your studying, but the point of writing simple notes is so you don’t have to remember them. That’s why you wrote it down!
If taking notes is important to you, then hotkey it. Be it PC or Smartphone. Hit a key(s) and you’re typing notes. So then why is it so painful to write a shopping list (or any other kind of note) on a Smartphone? If you’re not comfortable with the text input methods of your smartphone then maybe you need a different smartphone. And how much more battery life does it take to write up a list and review it later? It’s the same as writing and reading a text message.
Making notes for lenghty email discussions can be made the same way, if this is something that needs to be done.
The reason I set my Smartphone up to be this way is so I didn’t have to carry around a memo pad! Why is a tech site telling people to go back to paper when they don’t need to? You should be showing people how to ditch the memo pad, because it’s more than possible.