Surprisingly, there are not many free elements in the modern home. Copper water pipes, found in some homes, have been largely displaced by plastic products. Incandescent light bulbs which contain argon are being replaced by fluorescent and LED lights. Thermostats used to contain mercury; now they are mostly electronic.
In newer homes argon can be found between the panes of glass in windows, Americium is used in smoke alarms, the graphite form of carbon is in pencils (referred to as lead) and the diamond form is in jewelry, gold is in jewelry and electronics (although usually alloyed in jewelry), some cookware is made of cast aluminum, electrical wiring is copper, phosphorous is on the end of match sticks.
It is difficult to find a "pure element" anywhere. However, a large part of the air in any home would be oxygen. Even though the oxygen is intermingled with CO2, water vapor, and various other gases, it can certainly be found with the proper scientific equipment. The challenge would be to isolate pure O2. Even jewelry, such as high-carat gold, silver, or platinum in someone's home is not made up of a pure amount of any of those elements.
Perhaps the best answer is that you can find a number of pure elements if you have the right scientific technology. Presumably, however, the question requires you to not consider processing anything chemically so as to separate pure elements from the household environment or products.
There are many pure elements that can be found in your home, and many of them have the elements' name itself in the common household item's name.
(ELEMENT SYMBOL, ATOMIC NUMBER, FIRST IONIZATION ENERGY (kJ/mol), ELECTRONEGATIVITY, MELTING POINT (K), BOILING POINT (K)(standard pressure), DENSITY (g/cm^3)(at room temperature, 298K and 101.3kPa for gases), ATOMIC RADIUS (pm))
- Lithium batteries, an alternative to alkaline batteries. (Li, 3, 520, 1.0, 454, 1615, 0.534, 130.)
- Thermometer, which contains mercury. (Hg, 80, 1007, 1.9, 234, 630., 13.5336, 132)
- Copper wire, to transport water, etc. (Cu, 29, 745, 1.9, 1358, 2835, 8.96, 122)
- Catalytic converters in cars, which contain platinum. They prevent hydrocarbons from burning, as they are a room temperature catalyst. (Pt, 78, 864, 2.2, 2041, 4098, 21.5, 130.)
- Cadmium rechargeable batteries, which are, well, rechargeable batteries. (Cd, 48, 868, 1.7, 594, 1040., 8.69, 140.)
I hope that I've helped! In case you didn't know, at the top is a small reference to what the numbers and characters mean in the parentheses.