This is not exhaustive, obviously, but it's a handy overview. The full range of options are as unlimited as your own imagination and inventiveness, provide you think about all the aspects regarding weight, bulk, safety, accessibility, and cleanliness of the supply.
From bottom-end to top, some choices to get you thinking:
G.I. 1-quart plastic canteen.
Water for 6 hours or so. $5-10.
GI 5-gallon plastic water jug.
Water for 5 days for 1 person. $35-50.
Aqua-tainer 7 gallon water jug.
Water for a week for 1. About $20.
Water Bob 100-gallon bathtub water storage bag.
Water for 3 months. $30.
Food grade 55-gallon water barrel.
Water for 2 months or so. $75-ish. (Shop around. You can do better than this. Also, some opportunistic jackholes are asking $175 and more for the same thing. If you're willing to pay over 2 times market price, go to the tattoo parlor and have "SUCKER" emblazoned on your forehead.)
IBC 330-gallon caged palletized water tank.
Water for nearly a year for 1. Over $500 new, plus shipping.
Used ones can be had; make sure they were used for water, and not something like vinegar, or some toxic chemical. This is why IMHO, new is your friend unless you're a careful customer. Also nota bene the filled weight is nearly a ton. This mixes with stick-built upper floors in apartments rather poorly, especially in seismically active areas, but it will help you meet the downstairs neighbors. And their insurance adjuster.
OTOH, if you mount one on 3/4-5/4 plywood set on top of two levels of cinder blocks in a ground level garage or other concrete slab, the drain spigot will be handily elevated to fill smaller jugs and buckets. If you mount one or several in series at elevation, and plumb them to the home system, you can create low water pressure to supply whatever.
Various sizes. This one holds 425 gallons, and goes for $57 @ Wal-Mart.
You could get an 18' diameter x 52" tall metal-walled monster that holds 7700 gallons (a year's drinking water for 20 people) for a bit over $900.
Even bigger models are available. BTW, the best time to buy is now, with retailers and manufacturers sitting on last summer's leftovers, and sales prices in full effect.
Notes: if you can put it up inside a garage and put the cars outside, it's secure, and on a stable and accessible surface spot. You'd want to cover it, still be best off by purifying/filtering the water before drinking or cooking, and want to sandbag or build some diverters in case of leakage or failure. But you could cook and drink for years, and have enough left over to wash a set of clothes in a bucket once a week, and then use the after-wash to occasionally flush a plumbed toilet, even in a multi-level condo with garage in the 'burbs. Obviously, you wouldn't be able to leave it set up perpetually, but in a pinch, with between a couple of hours to a day, you could fill it up while the muni taps are still running. Think about that.
There are obviously even larger storage options, including in-ground pools and water tanks. As you approach that point, and get into the means to fill/recharge them manually or naturally, you're getting more into water sources than water storage.
Which I'll visit another time.