No. If your old battery has reached the end of the road and needs to be replaced, or if you think you need a battery with a bigger amp capacity for easier cold weather starting or to handle added electrical accessories (such as a killer stereo system, driving lights, etc.), then there's no reason why you have to install a battery that's the same size as your old one.
The word "size" may be a bit confusing here because what we're really talking about is the battery's amp or power rating, not the physical dimensions of its case.
A battery with a bigger case is not necessarily a more powerful battery. Battery manufacturers can cram a lot of amps into a relatively small box by varying the design of the cell plates and grids. So two batteries with identical exterior dimensions may have significantly different power ratings.
Batteries come in many different sizes and configurations (which are referred to as "group" sizes) because the vehicle manufacturers can't get together and standardize anything. So when you're choosing a battery, you have to consider three things: (1) the group size (height, width, length and post configuration), (2) whether your battery has top or side posts, and (3) how many amps will be needed for reliable cold starting and vehicle operation.
Because there are 57 different group sizes, many aftermarket replacement battery suppliers consolidate group sizes to simplify inventory requirements. So some replacement batteries may not fit exactly the same as the original. The battery may be slightly shorter, taller, narrower or wider than the original. But as long as it fits the battery tray and there are no interference problems (too tall a battery may cause the cables to make contact with the hood causing a dangerous and damaging electrical short!), it should work fine.
Some replacement batteries come with both side and top posts to further consolidate applications. Some also have folding handles to make handling and installation easier.
Though many replacement batteries are marketed by the number of "months" of warranty coverage provided (36, 48, 60, etc.), what's more important in terms of performance is the battery's power rating which is usually specified in "Cold Cranking Amps" (CCA) rating. The CCA rating tells you how many amps the battery can deliver at 0 degree F. for 30 seconds and still maintain a minimum voltage of 1.2v. per cell.
In the past, the rule of thumb was to always buy a battery with a rating of at least one CCA per cubic inch of engine displacement. But twice that is probably a better recommendation for reliable cold weather starting.
At the very least, you should buy a replacement battery with the same or better CCA rating as your old battery or one that meets the vehicle manufacturer's requirements. For most small four-cylinder engines, this would be a 450 CCA or larger battery, for a six cylinder application, a 550 CCA or larger battery, and for a V8 a 650 CCA or larger battery. Bigger is usually better. Extra battery capacity is recommended if your vehicle has a lot of electrical accessories such as air conditioning, power windows, seats, electric rear defogger, etc.
Most batteries are "dry charged" at the factory, which means they're activated as soon as acid is poured into the cells. Even so, the battery may require some charging to bring it all the way up to full charge.
Most experts recommend charging the battery before it is installed regardless of whether it is dry charged or not. This will ensure the battery is at full charge and lessen the strain on your charging system.
When the battery is installed, it must be locked down and held securely by a clamp, strap or bracket. This will not only keep the battery from sliding around on its tray (which might allow the positive cable to touch against something and short out the battery or start a fire!), but will also help to minimize vibration that can damage the battery.
The battery cables should also be inspected to make sure they're in good condition, too. If the cables are badly corroded, don't fit the battery posts or terminals tightly, or have been "fixed" by installing temporary clamps on the ends, the cables should be replaced. At the very least, you should clean the cable clamps and battery posts with a post cleaner, sandpaper or a wire brush to ensure good electrical contact. A light coating of grease, petroleum jelly and/or installing chemically treated felt washers under the cable clamps will help prevent corrosion.