Drive two scrapers between the wall and baseboard, then drive a shim between the scrapers. Work your way down.

How old is the house? Someone may have added drywall over plaster and ignored the baseboard. In that case you'll have to cut above the baseboard and possibly destroy a piece of baseboard to get started.

I believe anyone that tries to answer this question would have pried off quarter round and scraped caulk and paint from joint between wall and baseboard for a better view. I find it amazing that emily thinks people can better analyze it from pictures than had she took time to do a little scratching around first. When it's time to reattach baseboard I wonder if she will ask "what is the best way to drive nails"?

It looks like they drywalled ontop of it. In most cases for flooring you only need to remove the bottom 1/4 round to put new flooring then put it back on top of the new flooring. That would be my first choice. There is probably tons of paint on that baseboard as well as some lead paint so best to leave it and hopefully only replace the 1/4 round at the bottom OR replace it all with deeper baseboards so that it covers some of the drywall but that will require some spacers and a hell of a lot of work. If you are dead set on removing it run a knife along the top of the baseboard to separate it from the putty I see before trying to take it off. NOTE you will damage the walls. Count on it.

Hi, I fund the best way for me to remove base board molding was first score the top with a utility knife then remove the quarter round. Then using a thin pry bar with a thin foot on it, drive the foot of the pry bar about a half inch. under the bottom of base board and gently and a little at a time Pull the bottom of the base board out.

Good Luck Woodbutcher