As long as you are courteous, and everyone else is courteous there shouldn't be too much of a problem. Most buyers and agents have a mutual respect for the owner and/or tenant.
You can request a 24 hour notice prior to showings, or something else reasonable that can be agreed upon. You may want to ask a lawyer about tenant's rights if you feel this might be an issue. Remember that you are the guest (renter) in the owners home, and this does restrict you on what you can and can't do with or at the property. Owner's have rights too...including the right to sell their property. You will have to give up some of your privacy as you know, but people can't just show up unannounced and demand to be let in unless it's an emergency of course. As an offset to this inconvenience- you are getting a good rental rate, right? And a roof over your head...and a chance to hopefully catch up on some bills?
Being at the home when a showing occurs is generally frowned upon. Just imagine how awkward, difficult, and what a deal breaker it would be trying to sell a home when buyers are surprised by a dog licking them to death, finding people at the table trying to enjoy a nice meal, dirty laundry, and a recently used stinky bathroom (hey, when you gotta go you gotta go...but still embarrassing.) As a courtesy to everyone involved you should vacate the home and make it presentable for the showing if requested. It is a disruption to your life, but you are the owner's guest. If you decide you don't like the disruptions, and choose to be a disruption to the potential home buyers, the owner, or agents...the owner might kick you to the curb! Also, if you must leave the house for a showing and can't take Fido with you please put him/her in the yard on a chain, or in a cage, fenced in area, or room not significant enough for buyers to want to see...AND notify the owner and/or Realtor where the dog will be. If the dog attacks somebody...well...nobody wants that... (I'm sure your dog is a good boy or girl though)
On the other hand...if you are a fairly organized/neat/clean person there really shouldn't be too much inconvenience. If you choose to leave during a showing you won't feel rushed to get out of the house stuffing your personal items in drawers and closets, or sweeping dirt under the rugs if you keep the place nice. Sure, you might have to leave the house for an hour or two....but maybe Fido needs a walk anyways, or you take it as an opportunity to treat yourself to dinner and a movie. I've also heard a few stories of how tenants have actually helped sell the property by being at the home during a showing. If a buyer walks into a welcoming atmosphere, and a tenant who knows about the property is there to welcome and greet them it can actually go OK. Talk to the agent showing the home on that one- just to get their ok as a common courtesy. There are some legal issues involved on that one (having to deal with a non-licensed person providing information.)
Anyways, good luck. Hope this helps (I've been a renter in your shoes, and am a property manager and real estate agent representing buyers, sellers, and work to accommodate renters)