Top of the line-
Super Mario Land
Half Life series
DBZ: Budokai 3(I know, its a DBZ game, I must be a fanboy, but may I be struck by lightning if this isn't one of my favorite games, and I don't like any other DBZ game, so that isn't it)
Super Mario RPG
Super Smash Brothers Melee
Resident Evil 4
Mortal Combat(original, SEGA)
God Of War
Diddy Kong Racing
Metal Gear Solid(first PS2 version)
So, what sucks you into a game? With the recent advent of the battle of 2 different trains of though, namely, "graphics whores suxorz" battling the "The Wii is jsut flailing your arms, look, IM DOING IT RIGHT NOW!!!! LOLOLLOLO!!!!", I started to really think about what was important to have in a game to draw me into it. The answer, essentially, is that (surprise surprise) there are a plethora of ways that a game can amaze me. Something that, when you experience it in a game it completely blows your mind could be something as small as a piece of trash to the very foundation of the game itself. Its a question that gamers have been seeking the answer to for years and has no one "true" answer. However, I am going to list some of the things I have experienced in games that have truly made me happy to be playing the game, in no particular order. Also, there will be games used in multiple areas, that is merely because they are great games, and this is completely allowed, and should be done more often by developers.
Story You could argue(and many do) that this turns the game into more of an interactive movie than a game, but this is not necessarily true. A great storyline does not need to have intricate plot twists at every corner, mounds of speech or text, or hours of CGI footage(though a great number of them do). The main purpose of a great story is to get the player involved in the story to the point that there is real interest in what will happen next, and what the conclusion of the game will be(beyond merely "I win, hooray"). No matter what the graphics look like, no matter how awesome the control scheme is, no matter how fun the action is, none of these elements alone will draw you into a game more than an event like the death of Aeris in Final Fantasy VII or a certain realization in Knights of The Old Republic. With that criteria in mind, here are some of the games I have come across that accomplish the goal of sucking someone in with a great story: Final Fantasy VII and VIII and X(forgive me, I never played the 2D Final Fantasy games), Star Wars: KOTOR, Beyond Good and Evil and Parasite Eve.
Atmosphere This is a little harder to nail down than the story as an "aspect" of a game, but is important nontheless. Its essentialy the fairly unmeasurable but easily experienced "feel" that you get from playing a game. It is is a combination of things like storyline, backdrop, enemies, characters, music, etc into an immersive gaming experience. This is to say that it won't be like a turn based RPG where there is a phenomenal story that ends up being hampered by the clunky battles, the repetitiveness of the enemies, and the fact that you have to talk to some NPCs over and over again to get certain goals. This, however, isn't to say that a game has to be perfect in all areas to accomplish a great atmosphere. A game like Shadow of The Colossus, which had little sound, occasionally clunky controls, and only a small portion of the playtime set aside for progressing the story is a BRILLIANT example of how creating a great atmosphere can completely make a game worth playing. The game does this with the beautiful landscape that you traverse, not adding in any needless "travel music", creating a wonderful sense of scale and size, and using a good but fairly uncomplicated story. Some other examples of something adding to the atmosphere of a game include when guards talk to each other before they see you, realistic interactions between NPCs that appear to be part of a normal life(Oblivion), the NPCs in Beyond Good and Evil, and the visual level design in God of War II, where you will see places you were hours ago, sucking you into the idea that it isn't a linear game, but rather a world you are going though(though ironically it is just linear). Essentially, the designers recreated an experience through the medium of a game rather than just having a game explain the story they wanted to tell(which it also does). Some other games that have a great atmosphere include Ico, Beyond Good and Evil, God of War II, Half Life and Half Life 2.
Physics/processing power This has recently(along with controls) become somewhat of a heated topic, but the fact is that this does help with the immersion of a game. The better something looks, the easier it is to relate to it and therefore be drawn in. This covers a broad range of things from textures making backgrounds more believable, better lighting allowing for more realistic worlds, better faces allowing the emotion of a character to be shown more accurately, physics programming advancements leading to a better ability to represent a physically immerse world and even just the ability to have more "things" in the game, whether it be people and places like GTA, pieces of trash and movable boxes like Half Life 2, different car parts affecting the performance of a car in Forza/GT. More power allows you to add weight and physical properties to matter so that it will react as if it were the real world as well as create much more advanced AI which leads to many more enhancements and adds to the immersion as well as producing many "wow" moments. And, of course, there is the superficial stuff like textures and polygon counts, or even (as an older example) the ability to even have a game like Mario 64 be 3-D in nature. Some games that really seemed to put graphics and physics at the top of their priorities were Half Life 2, Final Fantasy VII, FEAR, God of War, Gears of War and Oblivion.
Social interaction The days of gamers all being complete nerds/shut ins are behind us, well, at least the days in which these were the ONLY people playing games. Games aren't necessarily a solo man against machine undertaking. They can be a 100 hour turn based RPG or a Zelda-like adventure game, but they can also be more of a group man against machine undertaking(co-op) or a social gathering that is only loosely a game at all(World of Warcraft). Some of my favorite games were games that I could play co-op with my friends, such as the old Turtles in Time game on the Super Nintendo or Final Fight, where I would work together with a friend to complete the levels. I can see the anger coming at me now, but at the heart of World Of Warcraft, and most of the MMORPGs that are popular now, is the interaction of the players with one another. The game is almost just a premise to get this widespread interaction and social hierarchy going. And this is the very reason that they are popular, because they allow interactions within a game that were never allowed before. The game that best fulfill this social interaction are any game with coop or WoW.
Competition This experience does not just pop up from making a game, then putting the ability for people to fight other people in. It takes a long process of balancing and designing to specifically make a game well suited for a fair multiplayer experience. And, some games just don't have the ability for multiplayer experience, simply because the genre does not lend easily to mulitplayer competition, such as an adventure or platforming game. This can take a game from a $50 purchase that lasts for 20 hours to a $50 purchase that will literally last for years. Competiton is a great way of adding longevity to the game by allowing for many, many adrenaline pumped moments of gameplay thereafter. I have often been emotionally moved by the storyline or wowed visually, but the adrenaline rush from extreme competition in a close match is not to be underestimated. Some examples of this are Counter-Strike, Starcraft, and Halo.
Control method A unique control method is probably one of the hardest things to come by in a game, possibly because a new controller is rarely made, but new ideas and new programming techniques are constantly being used to enhance the control scheme at least. However, this can also offer the most unique gameplay experience once it is utilized. It is used more often in arcades where large machines are common, but there are some instances of it in console gaming as well, especially more recently. DDR is a great example of this. The large pad makes the player actually move(most often terribly) to the rhythm of the music, rather than just hitting a button at the right time. Then, there is Guitar Hero, which actually have a very different controller shaped like a guitar to try to immerse the player into the idea that he/she is playing a guitar. And, of course, the most prevalent example of this is the light gun, which the player physically aims rather than relying upon a stick. This shouldn't be overlooked, as it is the only thing that we are physically touching as we are playing the game(aside from the couch or floor, of course). In fact, it was one of the reasons I actually liked going to an arcade, it had a variety of controls, from the sit down racing game complete with wheel, pedals, and shifter to the more conventional 6 buttons and a joystick to the light guns to the outrageous Gyroscope-like space games that actually spun you around(though I never actually played one of these). However, it would seem that there is no "best" control method, as each one works well for a group of games(or a single game) but few methods work for a very wide variety of games(namely, some sort of method with a few buttons and something that has a wider range of outputs, such as a mouse/joystick). Some examples of good control methods are the Wiimote(with nunchuck, though 4 buttons to replace the A button would be a nice improvement) and the PS3's Sixaxis.
Gameplay This is the hardest to pinpoint area that a game can excel in because there is such a wide variety of styles that people like. Even aside from the very easy delineations such as RTS, FPS, RPG there are subsets. For example, many of the fans of more "fast twitch" shooters such as Quake may not like the somewhat slower play of Halo, and someone who even likes both of those may not be a fan of a more tactical game like Counter Strike. And then, even if you have all of those sorted out, there are(especially more recently) a good amount of games that mix multiple platforms. For example, games such as Games like Beyond Good and Evil which include a myriad of different gameplay elements(which has adventure, mini games, vehicles, battle, photo collecting, and a bit of puzzle) or games like Shadowrun that simply tweak an existing genre. And, of course, you could lump "minigame games" into this category as well. Realistically, this aspect of gaming is just too vast to be able to nail into a few words. Logically, it may be true that this is just the "fun factor" that many people talk about and is simply a matter of preference, but I'll just say that I have no idea of how to explain how "gameplay" makes a game good other than a personal preference for certain combinations of the above aspects.
And so ends a long blog that wanders around and really doesn't say too much, but hopefully it at least got you thinking. If you managed to get through all of it(all 0 of you) let me know what you would add, or if one of these things doesn't seem that important to you. Post away!