In many ways, PC and console gaming are two sides of the same coin. Both present unique ways to interact with the games themselves, and some genres just feel better on one or the other. Despite being the same type of entertainment, there are some very real differences between the controls and experiences that PC and and console games provide.
Console games have been the poster boys for the industry for years. Most people started out on consoles, so it is no surprise that so many people just feel that gaming feels better on a console than on a PC. It's a matter of familiarization and adjustment. In many cases the control schemes for PC games confuse those who are not accustomed to having to work with both the keyboard and the mouse in something as fast-paced as first person shooters or other types of action games.
There is little denying that controllers have the advantage of being easier to use. The analog sticks, triggers, and buttons are plainly laid out and easily within reach. When playing PC games, the player must get used to using either the WASD or the arrow keys, and must familiarize themselves with those keys, any additional keys needed for the game they are playing, and simultaneous mouse movement. In most PC games it is possible to bind keys to the player's preference, but for many console gamers the transition from streamlined control-schemes to those that force them to learn a whole customized control scheme is overwhelming.
Because of the simultaneous usage of mouse and keyboard, the PC is has the upper hand in a few key genres. For instance, first-person shooters and real time strategy games are generally best enjoyed on the PC because it is their native environment. The dynamic between the large amount of in-game bound keys available, and the quick and seamless response time and movement of the mouse is what makes using a PC for gaming the choice for many.
Consoles are better for games that do not require precise control and micro management. Real-time strategy games often do not fare well on consoles, as Starcraft 64 on the Nintendo 64 demonstrates with clunky controls and even more cumbersome unit and resource management. This is a glaring example of how it difficult to manage several small tasks with a controller, whereas it is very easy with a mouse and keyboard.
Another benefit that PC gaming has above that of its console brethren is the player-made modification (or simply "mod") scene. There is a thriving and dedicated scene of mod programmers for many of the most popular PC titles. These modifications can greatly change the whole experience of a game. A very simple example of this would be map-making communities for real time strategy games or first-person shooters, though a far better example would be whole character model and scenario replacement in titles such as The Elder Scrolls: Oblivion.
Compatibility is an issue that many people struggle with in PC gaming, as many older titles do not work on newer operating systems. For some games there are hacks, mods, or work-arounds that force the games to work on Windows Vista or 7 (such as Fallout 1 and Fallout 2), but some lesser-known titles simply do not have the fanbase to come up with these solutions. This makes dual operating system usage or simply using an older computer a must for those who enjoy older titles.
Compatibility is something that console gaming struggles with as well, though in a different sense. Old video game consoles eventually die, which means they must be purchased again. Classic games are being ported to the Playstation Network, Xbox Live Arcade, and Wii Virtual Console, but those with physical copies of their favorite classic titles are left to purchase a replacement console.
Backwards compatibility can also be an issue. An example of this is the Xbox 360's lack of built-in backwards compatibility for original Xbox games. The console must be patched in order to play titles from the first Xbox console. Today's Playstation 3 models are only backwards compatible with titles from the first Playstation. Only the first-run 60GB models of the console can natively play Playstation 2 games.
There are benefits to both forms of gaming. Doing so on the PC allows for an enhanced player experience through more intuitive controls and player-made modifications, but it can be difficult to adjust into for those inexperienced with a keyboard and a mouse. Console gaming is easier for players of all ages and experience levels to get into, but presents the problem of having to buy a new console every few years for the newest games. It is up to the player's hands -- and budget -- to decide which side they will choose.