Summary: Evernote + gesture typing, unsorted and untagged.

Do you take any notes on paper? If so do you scan them or otherwise digilatize them?

No. Paper is cumbersome and unsearchable. I need my notes with me at all times, so I use Evernote.

Do you have specific strategies for deciding which information to write down?

Most often, I record details that would likely be lost after a mental context switch. Also, if I feel that I will need this piece of information in the future, I just write it down.

How do you write notes to capture all important information?

Evernote on Android, using gesture typing. (BTW, gesture typing will be introduced in iOS 8 in September, so this strategy will work on Apple devices too).

Do you tag your notes?

No. Basically, I have one dedicated tag, "booze", which I use to tag notes about wine (unlike whisky, there are hundreds of wine brands, so I have to remember which ones I liked). The rest of my notes are an unsorted mess. I rely on search for retrival. When I write notes, I try to include keywords that I'm likely to use when searching.

If you use Evernote, or a similar system how private are your notes? Would you allow friends to read in them? Your spouse?

Fully private. I'm a paid subscriber which lets me protect notes with a pincode.

Edit: Just wanted to add that if a note grows too large, I move it to a separate Google doc (also accessible via mobile).