There are many CASE tools, many software for diagrams, drawing, documenting. But can they replace old good paper?
Every day, all day! (Okay, not all day, but a lot)
I actually had a debate a while back on the value of psuedocode, and I was giving my input on how much pen/paper and some pseudocode could work wonders at times :)
I always find it easier to jot down what I'm about to draw/model before using application tools.
All the time I use pen and paper, I find them invaluable tools to programming! Making notes, etc, etc...
No software can ever replace the sheer ease of jotting down ideas and solution sketches using pen/paper! EVER!
Once you have your critical thinking down on a paper you can take your time to beautify them using fancy softwares and tools.
Especially when it comes to doing some math before the implementation, there's nothing better than putting it down on paper first!
All the time. When I want to draw/write something complex, I don't want to master a piece of software to do it. Also means there are no extra applications hogging up my system resources. Plus, there's something satisfying about writing at all angles on a piece of paper :).
I don't use pen and paper when working alone, but I always use them when working with other people, talking with customers and so on. I mainly use pencils to draw diagrams.
Using quick sketches is an invaluable tool in clarifying requirements with a client. You don't have to be Da Vinci to quickly encapsulate complex business logic or UI behaviors in some simple sketches. Leah Buley at Adaptive Path has great resources on sketching for UX. Programmers can learn these techniques as well. You'll save a lot of time using paper first, before sitting down in front of Visio.
I vastly prefer pencil & paper (or pen & markerboard) for real-time thinking. It can handle just about anything my brain thinks of. If I need to create any official artifacts, I'll take what I've drawn and set it up using a tool. But usually the initial copy is sufficient.
On a side note, I'm still not sure why just about everyone in college switched to laptops for taking notes. You don't have anywhere near the ability to express your thoughts in Word as you do on paper.
Most of the times when I program you can see papers all over my desk, some are wrinkled on the floor and some are not.
I usually do my brainstorming on paper and preliminary UML diagrams.
If only I had a whiteboard... :)
All the time, especially for complex logic with lots of conditional programming!
I use computers to solve easy design problems, but when I hit something really hard I break out the powerful tools - pen, paper and brain.