Long nights have been spent thinking about Quake, how it is dying, how it would be a shame for such a venerable franchise to be killed. Quake 4 certainly didn't help things with its lack of originality. Quake Live pushed the Quake 3 to the limits, but after 11 years even all the improvements can't keep the game from stagnating.
So here's what I would do in Quake 5, given a lot of resources, to significantly revamp the series.
Part I: Single Player
Time hasn't been kind to Quake's simplistic single player design. It's basically a series of levels where you shoot everything that moves tied together with a weak story. Storytelling and game design has moved leaps and bounds since the first Quake came out. Quake 4's campaign looked like it took a lot of time to make, with its voice acting and large number of unique models, but it was resources wasted on dated game design.
Oh look, a gun that shoots lightning. How original... 15 years ago.
What I propose is to have a single player that's completely different from the multiplayer, much like what Blizzard did with WoL's campaign. Instead of traveling through linear levels strafing and shooting dumb AI enemies in the face, we can have a single massive labyrinth that the player has to go through. Players explore the dungeon trying to pick up weapons, ammunition, and other things such as expanded health/armor/ammunition capacity to grow their character as they face stronger enemies deeper in the dungeon. Think Metroid Prime type exploration with faster movement and rocket jumps. Design-wise, this type of campaign would offer several advantages.
One big advantage is that this type of level design would take full advantage of Quake's robust movement system. Levels can be made with ledges and platforms that provide incentives for players to learn multiplayer techniques such as strafe jumping, rocket jumping, plasma climbs, etc. Secret areas reward players who have mastered these mechanics and can put them to good use. Various surfaces can be designed to facilitate certain types of movements, such as walls that allow for higher rocket jumps and so on. Quake's movement system also facilitates speed running, which is a common feature in Metroid-type games. If anything, Quake's movement system is even better suited for Metroid type games than the Prime series themselves, since it allows for more dynamic, fluid combat. It's surprising no one has tried this yet given the success of the Prime games.
Space jump is for pansies. I just shoot myself in the foot with a rocket launcher.
Another advantage is that such a campaign can offer a lot of diversity for bored gamers. The dungeon can be partitioned into zones with their own themes much like Metroid. Areas can be "unlocked" by either placing terrain obstacles (such as requiring the rocket launcher in order to reach a high ledge) or by having doors that open in response to specific weapons fire. Boss fights can be a mixture of the usual massive boss with the single weak point and "duel bosses", which are essentially multiplayer maps that teach the player how to duel in multiplayer while they're playing single player. Simple, rewarding, unobtrusive.
Finally, this type of single player campaign allows for potential sequence breaking, which is IMO one of the most exciting aspects of Metroid type games. Sequence breaking is when one exploits the physics engine of a game to reach areas of the game sooner than the game designer has intended, opening up access to powerful weapons sooner than intended and thus increasing the number of ways a game can be replayed. This type of beneficial oversight has lent longevity to some of the best games of its type such as Super Metroid and Metroid Prime. Of course, in order to do this, designers must purposefully not include "invisible barriers" in their game whose sole purpose is to bar players from accessing areas that look accessible, but actually aren't.
Part II: Multiplayer
This is the difficult part. Quake's multiplayer is the epitome of fast-paced competitive FPS. How do you improve on something that's practically perfect already? Well, if we looked at Quake 4, dumbing the combat down certainly isn't the solution. The most promising solution then is to shift the game the other way: to make it even more frantic and fast paced.
No, not like this
When designing the sequel to any "legendary" competitive game (Quake, Brood War, Counter-Strike), one must always keep in mind the highest echelon of competition. These are the players who will charge out the gate of any new game and still be the most skilled. They will be the first to exploit all possible facets of the game, to abuse the most broken aspects of a game, "figure the game out". Games that are "figured out" tend to stagnate and die. Therefore, it is the job of the designer to shake things up as much as they can to hold the highest echelon of players at bay to prolong the life of their game.
To "shake things up" in Quake, obviously slowing things down is not the way to go. Professional players are already able to make insane rail shots with a flick of their mouse. But making the game too fast would also be detrimental. It would raise both the maximum skill ceiling and also raise the initial learning curve of the game for newer players to discouraging levels. Here are a few ideas:
1) Increased verticality, as well as methods and incentives to change altitudes. Quake 3 already has a lot of verticality in its levels, but we can do better. Verticality helps increase the skill ceiling by adding larger areas for players to attack and be attacked. Players will need to aim both vertically and horizontally to frag their enemies. Additional weapons and mechanics can be used to help players get to these higher places. One easy change is to reduce the self-splash damage done by rockets, allowing for more frequent rocket jumps.
2) Player imbalances. In all the earlier Quake games, players could change their skins, but the basic character that everyone uses has the same movement, health, and armor. Quake can easily diversify this by providing various different customizations with pros and cons such as more armor vs more health, bigger/smaller ammo capacity, movement speed, etc. Even if eventually professional players figure out which character types are definitively the best at the highest level, the diversity can still help elongate the game's shelf life among casual players.
3) "Casual" game modes that allow players to duel with their souped-up single player characters. Again, this is to cater to the casual gaming community and give them something fun to do while providing more replay incentive to the single player campaign.
These are just some of the things that can help create a focused, fun, and fresh multiplayer without having to resort to gimmicks such as vehicles (I personally don't like vehicles, since vehicle game modes tend to distract players from the core game play like DOTA does with WC3. Maybe resources can be made available to modders to create their own vehicle modes, but packaging vehicles with the game to begin with would be like... if DOTA came with WC3 from day one). And hopefully it'll stump the progamers for a long time too to keep the e-sports scene alive.