Chipping in my few cents here on a couple of issues.
First, “offline” vs “online” gaming. The thing is that there’s no such thing. The only truly “online” games are MMOs and their ilk. If you can play it without being online, it’s not a true online game. Halo is -not- an online game. It’s a game with an online component, and that’s an essential distinction that needs to be made. Many games will eventually probably have an online component, which is something I’m all for, because I’ve always felt the world needed more multiplayer games (particularly multiplayer co-operative games, actually). While nothing will ever compare to being in the same room as your buddies and playing something and being able to yell back and forth, online is a pretty okay substitute, and has the advantage of being able to play with random people whenever you want. (and the disadvantage of playing with random people too.).
On the -other- hand, -lots- of games simply don’t lend themselves to this at all. Puzzle games don’t play multiplayer. CRPGs turn into the ghastly muck that is MMOs. Oldschool shooters and platformers don’t gain anything anything either. This is why we are seeing this horrible glut of bad RTS/FPS games right now that lead the OP to make this thread. There are large portions of the gaming population that are not remotely interested in the sorts of games that -work- online, and the “everything must have online play” mentality in the gaming industry is driving a lot of these folks away… because it leads to the creation of more FPS’s and RTS’s and MMOs. Sure, you can add “online” features like downloadable content, or leaderboards or something to some of the underserved game types, but it’s not online -play- and it never will be. The games are simply not designed to be played by more than one person.
There is a large chunk of the population that is -not- served by online games, and a lot of indie developers are fast figuring that out. And so am I, as I find myself digging up all sorts of absolute -gems- in the PC gaming space which I will -never- connect online for more than a patch download.
Online gaming is, as has been said by others, inherently limited. There are certain types of games that simply do not work there. In fact, I’m going to go so far as to say that more games do not work effectively in an online context than do.
Single player games, on the other hand, will never meet the needs of the people like some of the other posters here, who appreciate online gaming for its ever evolving challenge. I don’t expect game AI to compare favorably to humans in my lifetime. And as mentioned, online play is great at giving you at least some of the sensation of playing a game with your friends. So I dub it completely impossible that either online or offline gaming will ever “win”. The concept is as absurd as monopoly beating out soccer.
Nextly, for Lamia (and others who may be interested, of course), just a few bits of suggestion. If you like the “novel” style of gameplay (Which is to say, you have no concern about ‘linear storyline’ (Hah) or fastpaced game mechanics), I think I have a few suggestions. Firstly, a broad suggestion - you seem like you might like CRPGs or JPRGs (Computer RPGs and Japanese RPGs, respectively, to differentiate between the likes of a Fallout from, say, a Final Fantasy). They’re about the story, largely, and while there may be some puzzle solving elements, they are generally not the focus of attention. Combat may involve some ‘action’ depending on the game, but again, it’s unlikely to be the focus. And some ‘statbuilding’ is involved, but in a well designed game, it should be seamless - an element of gameplay in the sense of “Oooh! I got a new ability!” as opposed to “Damnit, I need to grind out five more levels before I can advance!” Largely, the focus is on the characters and the unfolding of the story. In the JRPG space, I suggest the Tales of… series, available in modern incarnations on PS2 (Tales of the Abyss), Wii (Tales of Symphonia: Dawn of the New World) and Xbox360 (Tales of Vesperia). For CRPGs, I can recommend, other than the aforementioned Fallout and Oblivion (Actually, both of those are me recommending on Hearsay), and on a smaller scale, Eschalon Book 1 (Available on PlayGreenhouse.com) and in a bit of a retro throwback, Ultima V: Lazarus, which is a remake of the legendary Ultima V using the Dungeon Siege engine. (Must own a copy of Dungeon Siege, but they can be had for about $2 on Ebay). Which segues nicely into my other suggestion. Which is, well, keep your eyes open for retro games and remakes. Such as the aforementioned Lazarus, it’s relative, the Ultima 6 project, and the recently released VGA remake for Quest for Glory 2: Trial by Fire.
Additionally, there are a few ‘adventure’ games out there for the various consoles. The most legendary (if you’ll pardon the pun) is the Zelda series, for various Nintendo consoles, though I personally cannot recommend Okami (PS2, Wii) strongly enough. Though some semblance of reflexes is required, the game is very forgiving… and, frankly, proof that A) People still can make amazing, innovative games. B) Games -are- art. C) Online games will never be the end-all, be-all. 
Hopefully that helps.
and play Legend of Zelda: A Link to the Past (adventure game) and Chrono Trigger (JRPG), awesome games.