As for dungeons, the idea that jumps right to mind is Aperture Labs, in which a player can attempt to uncover powerful technologies hidden behind faulty droids, complex puzzles, and many testing chambers. At high levels, players can even collect slices of cake that can be turned in for epic loot.
The Half-Life games are riddled with dungeons of all kinds, ranging from dams, to antlion burrows, to the Citadel. If there's anything the Half-Life series does well, it's creating iconic locations and giving you a good reason to go check it out.
Professions: Professions are one of the elements in Half-Life Online that I really see as having a lot of potential. If the game was hosted on a heavily updated version of the Source engine, applying a rule-set to that used by Garry's Mod for each of the classes could lead to an extraordinarily powerful sandbox system. Depending on their class selection, players can learn schematics to build pre-arranged units such as houses, cars, or chairs, or build their own things using the already-designed systems that players can use in the Source engine currently.
Each class would gain instant access to certain low-level schematics related to their profession, and could learn more complex and diverse skills as they leveled up. A Robot Engineer, for example, could start with a small pet robot and continually (through gaining experience and experimenting with crafting) unlock new upgrades for the robot, incrementally increasing its power, size, and capabilities. A Detective might begin with an investigation lens that eventually upgrades to have heat vision, patrol layout guidelines, or grant bonuses to combat against researched foes. Though this system locks players into only learning skills related to their class, the grid system outlined below allows players to explore whatever aspects of each class that appeals to them the most, and if schematics were an aspect of the grid sphere, players could choose which schematics they wanted to learn first, granting increasing flexibility over time.
Talents and Skills: I imagine Half-Life Online would feature a sphere-grid style of class progression, with skills tied to different class grids that players can navigate between by spending skill points. When players select their base class, they begin with 1 point in their class' region of the sphere grid, which they can then choose to navigate as their character unlocks more skill points and advances in power. Players can navigate between their class' specializations as they wish, or even explore towards the grid of other basic and specialized classes. Because all of the classes are on one gigantic grid, it would be possible for a player to take as few or many points in their base and specialized class' before changing directions and exploring towards other base or specialized classes. This will allow players to create characters with all of their favorite features, while still balancing out the power with the high cost of extending to that part of the grid.
PvP Possibility: Half-Life is based on the Source Engine, and not only had its own successful multiplayer platform, but also was built in close proximity to Counter-Strike, one of the most successful online PvP games of all time. The Source Engine is more than capable of handling games with complex rules or unique maps, and Valve has more than proved that they can create balanced, competitive multiplayer games. If the skill grid included skills that helped characters to excel in PvP situations, the diverse builds could lead to a complex meta-game, such as in League of Legends or StarCraft 2.
Subscription vs Free-to-Play: Valve has been a big proponent of F2P games for a long time, and I think they'd go the same route with Half-Life Online. They've proven time and again (Team Fortress 2 and DOTA 2 jump immediately to mind) that free to play can be a successful model, and doesn't need to diminish the quality of the game at all. As an MMORPG shooter (akin to PlanetSide or Firefall), there is a large market for microtransactions, featuring items such as cosmetic upgrade or convenience items. If Half-Life Online's market was connected to Steam, it would be even easier for them to find fiendishly clever ways to milk your dollars. Don't forget, people, these are the guys that host the Steam Summer Sale.
Likelihood and Prediction: 0% -- Pipe Dream. Even if Valve was interested in making a Half-Life MMORPG, Half-Life 3's production schedule indicates that it wouldn't be ready until most of its fan base was getting into their mid-life crisis (or perhaps it's perfect timing...). Valve is not a company to release a game until its perfect, and MMOs require a long production time besides. The amount of resources required for them to make a game they'd be proud to release about the Half-Life universe would never be worth the risk of failure for a company like Valve.
The only possible source of hope is the announcement made earlier this year by Gabe Newell and J.J. Abrams about the possibility of a Half-Life universe film, which indicates that Valve hasn't completely forgotten about their first-born child. Though it's a long shot to hope that Half-Life 3, or any addition to the Half-Life universe will be on its way anytime soon, there's a hope that an announcement will come sometime after the launch of the Steam Boxes and SteamOS, which will be released in 2014.