Yes. You can paint over wood paneling. But you must use sand paper and primer on the surface in order for the paint to properly adhere to the glossy surface of the paneling you have. And yes, you can fill in the grooves as you mentioned if you wish. It is up to you on the ultimate look you want - don't be afraid to experiment if you are looking to do something more interesting and fun.
Since you said this is in every room of the house - we suggest that you use a flat matte water based paint for most rooms. If you happen to have paneling in a kitchen or bathroom where the walls would be exposed to moisture, water, or in the case of a kitchen - oil or food splatters from cooking, we suggest an oil-based paint so that the surface is easy to 'wipe clean' and maintain (much easier to do than a flat matte waterbase that is porous and only absorbs the stains).
When you go to your local home improvement store, the folks there will be able to show you the proper tools to use to achieve any fancy paint designs or looks you wish to do. There are all kinds of techniques these days from sponge, to swirl texture, layered, etc. Painter's tape is also very helpful if you end up creating a look where you paint 3/4 (ceiling to 3/4 of the way down) one color and paint a slight shade different for the bottom and use divider crown molding. If you choose do to this, you can actually leave the grooves of the paneling for either part for a different look, too.
Good luck and have fun!