My daughter needed A LOT of baby proofing! Now that she's 26 months, it's much less of an issue. But I was shocked when we were visiting friends and their son (about 3 months older than our daughter) would play with toys next to computer cords, laptops, piles of mail stacked on the coffee table, remote controls, etc... All this stuff would have been in my daughter's mouth or knocked over/played with. She also would climb on furniture and roll off, or push chairs around and fall over, so we had to think about that too! We had a gate enclosure set up in a safe area of our living room from about 6 months to 14 months or so. We still have gates at the top and bottom of the stairs. Lots of objects needed to be moved up and out of the way so that she would not grab them. Our house is tiny and the kitchen has open spaces instead of cabinets, which was a HUGE pain because she would be in there grabbing everything and my husband has not had time to take on the project of remodeling the kitchen. So we had to do reorganizing there, too. Now she is less interested in all that stuff, but still very curious and exploratory with objects. It's interesting how each kid is different!
Another random note - if your baby seems very mobile and sleeps in a crib, and you're concerned about her climbing out at some point, sleep sacks (we have a Woolino one) are a great way to discourage climbing in the crib. They are also super cozy. My daughter loves hers.