We did: the outlet covers; babyproof things for the back of the doors, where the doors hit the walls--they are all 1 piece so there is no chance of the head of those things coming off and choking a little one; cabinet and drawer locks in the kitchen; "permanent," strong gates for the top and bottom of the stairs, and removable ones to use as desired between some of the rooms on the first floor (where there are no doors between any of the rooms, other than the bathroom and laundry room); and babyproof door knob things to go on top of the door knobs, so the kids could not open their closet doors or the pantry or bathrooms or laundry rooms on their own. A friend with an older child said her son put his stuffed animals in the toilet, so we bought toilet locks, but we didn't really need them as we just had the door knob things (which sometimes weren't so easy for the adults to use, too!).... Very important: secure any high furniture. We secured our bookshelves, floor lamps, etc. so they would not fall on the kids. There was a local girl who died a few years ago when the tv fell on her, and there has been a big movement about securing those, too.
We babyproofed when our oldest was about 6 months old, I think. She started crawling soon after, then pulled herself up soon after, then walked by her 1st birthday...and it happens so quickly!
Have fun!
ADDITIONAL INFO I JUST THOUGHT OF (after reading some other responses):
We had the corner guards. The ones we had worked wonderfully. It was soft thing that were eleastic, went around our tables (coffee table and end table in den/playrom), and did not damage our tables at all.
We have a tile area right in front of the den fire place, and we placed 2 comforters on top of that area.
We had gates preventing the children from going into the living room, so we did not put anything down on the tile in front of the fireplace in that room.
We really liked the kind of babyproof things we used on our drawers and cabinets. We had to install them, which is a pain, but they never broke, worked extremely well, and the kids could not get into anything.
Definately do the blind cords...that's a biggy. We also had things on our 2nd floor windows that only let the windows go up so far, unless we manually changed the settings.
How much you do may depend on whether you are home with your child all the time, or if others will be watching her at times. I had a sitter in the home 2 days a week, and I did not want to take any chances, and so we babyproofed so that we could be comfortable.
Also think about where else your daughter may be without you, like at grandparents' homes. We did some babyproofing at the grandparents' as well...blind cords, window things, etc. We had gates there as well. We also owned a travel gate (collapsable) that we kept in the car and took with us on trips, to the grandparents' shore home, etc.
Have fun with this!