I have a laptop with a VGA port - can I connect it to a Raspberry Pi using an HDMI to VGA converter, like connecting laptops to projectors?
no, the Raspberry Pi's HDMI connector does not allow for input, try looking at USB dongles that accept video and work with the Pi.
What exactly are you trying to capture?
Depending on what your laptop is running and how much effort you want to put into it you can tunnel X which allows you to display applications on a different computer than the one they're running on.
I've had some success on both linux-to-linux as well as linux-to-windows. If you really want to get fancy you could actually get a network crossover cable that allows you to create a system-to-system network so you could just connect your laptop and your Pi directly.
Alternatively you could also use something like TinyVNC which should run pretty quickly in this scenario.