Late model vehicles have many computerized systems; in most cases, each system is under the basic control of its own computer (module). There can be more than twenty modules on each vehicle and many of these modules have some sort of "learned" memory, which may be lost when the battery is disconnected. This can cause something minor, like the clock to lose its time, but it can also lead to engine stalling or even a failed smog inspection.
In order to avoid this issue, it has become more and more critical that power is supplied to the electrical system while the battery is disconnected, for any reason, including replacement. Luckily, there are many "memory saving" devices available that can be connected to the cigarette lighter or the OBDII diagnostic connector. These devices will supply enough power to the modules while the battery is disconnected so they don't lose their memory.
Be sure to follow all manufactured directions if you use any of these "memory saving" devices. Most of these devices use a small battery to supply power. Opening a door or turning the ignition on with the main battery disconnected can cause the battery in the device to lose power as well.
Here are some examples of how different modules can be affected by loss of battery power:
Loss of express-up feature due to loss of stored "pinch point"
Engine control module (ECM, PCM, VCM)
Loss of learned idle speed which can cause a stalling condition. Resetting of emission monitors can cause a smog inspection failure.
Power seat modules
Loss of "learned" seat and mirror positions
Loss of time, radio stations, and possible anti-theft lock out.
Transmission control module
Loss of adaptive information; most late module transmissions "learn" how you drive and "learn" to shift accordingly.