If you only need to balance audio for use in a home entertainment system (such as a home theater or surround sound system), there are a number of kits available. Brands such as Marantz and Denon produce XLR audio balancing kits and digital/analog receivers. These usually allow the user to plug in a single input and receive a number of outputs to be routed to various speakers. They also usually provide channel switching, allowing a user to quickly switch between inputs. For instance, you could switch between a cable box, a DVD player and a video game system. These systems also provide routing for video. A wide variety of these kits are available.
A mixing console allows for very precise audio balancing. Typically, mixing boards have a large number of input and output channels, as well as features such as EQ, faders and effects. Mixers are typically used in applications within a musical context; for instance, they are a vital part of both performing and recording music. A mixing console is only useful if you have need advanced sound control over a number of channels. It is not suited for simpler tasks such as home speaker systems.
A recently popularized alternative to analog mixing and sound engineering is the digital solution. There is a vast amount of software available, both freeware and commercial, that can balance sound for any number of applications. From simple programs such as Audacity and GarageBand to more complex programs that simulate soundboards such as VirtualDJ, there is software out there for every audio mixing need.
There are few alternatives to those provided previously that are still technologically relevant. Older systems for balancing audio do exist, but are unlikely to be as reliable and useful as the equipment and software available today. However, there are a number of variations of today's equipment, such as digital receivers with multiple inputs and basic EQ, to allow some of the functionality of a mixer while retaining the convenience and relevance to home entertainment.