Now, my version of TeXworks is 0.4.5r.1280 and I can't have the " character on the keyboard.
I have `` or '' instead. Why?
And It's the same with Alt+034. I'm very disappointed with that.
TeXworks has a 'Smart Quotes' mode that deliberately changes " to either `` or '' using some context-dependent 'cleverness'. This is available as " is very rarely needed in a typesetting context. However, the setting is easy enough to turn off.
For a single file, you can go to Format -> Smart Quotes and choose None: this turns off the auto-conversion for the current file. To turn it off generally, go to Preferences (Edit menu on Windows/Linux, TeXworks menu on the Mac) and select 'None' under 'Smart Quotes' on the 'Edit' tab.
"into``or''(depending on the settings).``for a opening double quotation mark and''for a closing double quotation mark. TeXworks is trying to be helpful by "autocorrecting" you on the fly. (See, for example, tex.stackexchange.com/questions/531/…)