Do psychic vampires exist? If so, what can we do to protect ourselves?

Yes, they do exist! Let's try for a definition first: Psychic vampires feed off the life force of other sentient beings.
Why would they do that? In my experience, the class of entities that feed off others are like parasites: they drain their host of life force energy, but may not even be fully aware of their acts. It is simply who they are, what they do. These entities are by nature parasitic, i.e. they need a host to support their own existence.

How do we attract psychic vampires?

When our auric field has been depleted by traumatic circumstance (illness, loss of a loved one, etc), we become more vulnerable to other beings. Also, in the case of accelerated personal evolution, the light we give off becomes more 'visible' to other beings. We are susceptible to become "food" for others that are lacking in life force energy and are looking for hosts to attach to. Many of these beings are not 'evil' by nature; they simply look for energy food as a means of survival.
What can we do to protect ourselves?

Towards the end of my day, I always like to look back on the past 24 hours: what did I like about this particular, unique, God-given day of my life? What bugged me?

I honor my energy by evaluating what worked, what did not; what made me feel happy, and what were the things/people/events that made me feel uneasy. Those three hours shopping for yoga clothes drained me much beyond the fun of having found a few comfy and useful clothing items. A call from a friend who prefers to ramble off long list of complaints about the injustices of the world made me feel tired. Taking a walk on the beach with my beloved and playing with the cats increased my happiness index.

We all have a list of "to-do's", and sometimes just getting a chore done feels wonderful; completing a project I've pushed away for some time is immense relief. But when the 'doing' takes over the 'being', I know I am in trouble, because I am not honoring my need for quiet time and quality moments.

Here's a suggestion: I invite you to look at the 'energy zappers' in your life.

Make a list of all the stuff that is generating irritation energy and tackle the list, one at a time. Sometimes even seemingly trivial things, like replacing that burnt-out light bulb in the laundry room, can be draining if they show up on your planned activity lists for too long. When I take just an hour each day to finally sow on that button on a favorite shirt or clean out the 'miscellaneous' kitchen drawer, I feel clearer, lighter. There is more energy available to do the things that matter.

Warning: beware of the need to get 'everything' done on your list all at once! While there are some days that we are happily exhausting ourselves cleaning out the garage and enjoying the results, I find it easier to move little rocks, one at a time. Above all, make time to nurture your Spirit! One hour a day of quiet reading time with an uplifting book, or listening to that wonderful guided meditation journey that you've wanted to explore for weeks, or simply sitting on a big boulder in a nature preserve and taking in the sounds of the birds and the bees with no agenda at all: that is quality time spent 'being', that is what feeds our spirit.

Make a list of your energy zappers, take care of them one at a time, and enjoy the healing energies of being. Emotional balance and improved body-mind health may be your best rewards.