For missed and underrated gems I'd say;
King of Fighters Maximum Impact 2 - King of Fighters with 3D characters and simple depth gameplay and parrying. It's just a lot of fun to play. Helps too that it has characters from other SNK properties.
Metropolismania 2 - Overly simplistic and something infuriatingly unfair and tedious but damn if the game isn't just insanely addictive. To elaborate, it's Sim City with the ability to go around and talk with every citizen and in doing so have them recommend other residents to invite to life in your town. After which you just put the house down, with no kind of currency limit. It's all about social networking and trying to remember what kinds of residents are most likely to recommend the kind you need (Because you do need hospitals, police stations, groceries, pre-schools, schools, high schools, parks, entertainment, offices and factories). The goal of the game is simply to get enough residents and meeting various criterion for what kind or how happy they are (i.e, good placement in your town grid to be close to everything they need). And best part - You could buy your own house and kit it out with various furniture as well as change your avatar into various outfits. It sounds silly, but it's just a relaxing and rewarding experience.
I would love to have a sequel in the same vein, but with less frustrating dead ends for contacts (That is, no one in town can recommend the resident you absolutely desperately need, or one of them can and you have to go through 150 different residents to find them, ask them the right questions or first become friends with them by giving them gifts or just talking with them enough times).
007 Nightfire - Best James Bond game after Goldeneye. It's just fantastically well made, apart from some extremely appalingly crappy vehicle based levels. It also has a fantastic multiplayer mode (With bots!), sadly plagued by arbitrarily restrictive character selection. The MI6 team can only have good characters and the Phoenix team can only have evil characters. That's dumb but it doesn't sound like it would be that much of a problem, right? Well, it is when there's a grand total of 3 good characters. It also doesn't have a LAN functionality. Also note, I'm talking about the console version. The PC version is absolutely awful.
Metal Slug Anthology - Not as much overlooked or underrated as it's just old. But these games are still good and should be played.
Breakdown - Exclusive to the original Xbox, this game is just insane. It's a first person action game where the focus in on hand to hand combat. Gun play is auto-aim based and barely relevant past a certain point of progression. The story of the game is it's highlight though. It's just an epic story with mindscrewy twists and lots and lots of memorable moments along the way. If you have an original Xbox still you owe it to yourself to play this game. Word of warning though - It's really damn hard. No one will think less of you for playing through it on Easy just for the story experience.
Call of Cthulhu Dark Corners of the Earth - A great horror game that I suspect that many might have missed. It is dreadfully buggy however, especially the PC version. The PC version is also extremely unstable with multi-core CPUs. To get it stable you need to run it with a single core and even then it can decide to crash on you. Get the Xbox version if you can.
Timesplitters 2 - Best console shooter ever made, bar none. The only issue is the control, which despite using two analog stick has the same non-fixed crosshair as Goldeneye had. It takes a lot of getting used to. The PS2 version of the game is by far the superior one, as the Gamecube and Xbox version have weird deadzone issues with the aiming. But people have reportedly gotten used to them. I can't. I own it both on Xbox and PS2. I Specifically bought the PS2 version for this reason.
Commandos Strike Force - A WW2 shooter/stealth game. As shooters considered, it's not the best. As stealth games considered, it's not the best either. But as a mix of the both, it's fairly unique. In any one level you get to play as two characters out of three, and can during the mission swap between the two ones in it at any time (Aside from a few instances where you need to do something as a specific character first). The characters are Commando, Sniper and Spy. Each have their own unique ability you need to use to progress through the level. Commando can dual wield guns and use all kinds of them. The Sniper can use sniper rifles and throwing knifes and can use bullet time when scoped. The Spy can silently stab or shoot with a suppressed pistol and take the uniform of enemies to infiltrate areas. It might sound disjointed, and it is a bit. The enemy AI is also not great either. But it's just a lot of fun to go around shooting and sneaking around to take down the Nazis. It also has one of the best varieties of setting in any WW2 shooter. The only such game I can think of where you actually go to Nazi occupied Norway. Worth checking out.
Far Cry Instincts - Best Far Cry game to this day. Yes, I'm saying it's better than Far Cry 3. It's far more linear, but it's extremely well paced and has impressive set pieces. Only on original Xbox (Notice a trend with my selection?), but definitely worth checking out. Far Cry Predator for Xbox 360 includes this game and the fairly mediocre sequel Evolution. I can't say if that version is good since I don't own it.
Psi-Ops the Mindgate Conspiracy - 3rd person shooter with psychic powers. It's just a great game, even if the story is goofy. A lot of memorable characters and cool powers that are fun and easy to use. Sadly, the game ends on an awful
cliff-hanger and since Midway went bust, it's never likely to be resolved.
The Punisher - This is how to do a comic justice as a video game. Infinitely superior to the movie. Yet, it's voiced by the same actor, which does an excellent job voicing the character but just looks too nice to play as him in person (That or the writing of the movie was just terrible). It's akin to Max Payne, except with less whining and more extreme cruelty against criminals.
Unreal Championship 2: The Liandri Conflict - A 1st/3rd person spin-off of Unreal Tournament for the original Xbox. It manages to blend melee combat and gunplay extremely well and offer a lot of content to play around with. Unlike standard UT though, characters have unique abilities (Base stats and abilities that are manually used that use adrenaline you pick up) and unique back up weapons and 2 weapons you select at the start of a match (Energy and Explosive), with only ammunition found in the levels. Downsides is that the game doesn't let you assign bots to teams, so you can't set up matches with uneven teams. There's also no domination mode and the inability to change weapon loadout mid-match is far too restrictive. Still a fantastic game worth playing.
Urban Chaos Riot Response - 1st person shooter with a cover system you always bring with you. At any time you can press L to put up a riot shield which stops any attacks that hit you. With this shield and lots of cool guns you need to take down the Burners, which is an anarchic gang of arsonists and lowlifes, constantly spouting taunts and profanities at the protagonist and all sharing the same dress sense, in that they all wear hockey masks. Does that sound awesome to you? Then play this game.
Gods Eater Burst - For the PSP. Best Monster Hunter-like game there is. Awesome sense of style, great setting, lots and lots of big monsters to kill and resources to grind. It has a distressingly low amount of game environments that simply repeat across missions. Enemies also have a bit too much health than I feel they should, which can make solo play a rather tedious experience. Much better played with friends - If you have a Vita, you should buy this game.
Armored Core: For Answer - Fantastic game if you like high speed mech combat and hard to decipher statistics. It's hard as all hell too. Downsides is that the story feels rather void of character. It has a very interesting setting but it just doesn't make the most of it. What it does have however is some extremely cool giant mechas to fight, as well as other NEXT Armored Cores (The kind of robot you pilot) to duel with. I'm guessing 4 is very similar to this, but I don't own it (I want to though, just can't find it for a decent price).
Global Defense Force (PS2, PSP), Earth Defense Force 2017 (Xbox 360, Vita) and Earth Defense Force 2025 (Xbox 360, PS3 - Soon Xbone and PS4) - They are just great. 3rd person shooters with a ridiculous amount of guns and levels to blast apart giant bugs, godzilla expies, robots and space ships trying to invade earth. Suffers from consistently poor frame rates however. It is one of those series of games that are awesome in spite of their obvious flaws. Stay clear of EDF: Insect Armageddon though, since it's an extreme downgrade in terms of scale (The other games have wide open levels you can freely roam - IA has slightly wider corridors with invisible walls all around) and entertainment value. The guns are just dull in IA as well.
Lost Planet 2 - Awesome 3rd person shooter with big bugs to blow up, robots to pilot and extremely ugly character designs to mess around with (Customizable characters universal to both singleplayer and multiplayer). Also has co-op, which is a ton of fun. Did not nearly get enough love when it was released.
Tenchu Z - Ugly, repeated levels, a bit awkward controls, limited to a single save, limited character customization. So what does it do right? It makes you feel like a ninja and give you a lot of cool abilities to play around with and tweak which you abilities and tools to equip as well as set your base abilities.
Ziggurat - Just... Go buy it right now. Or read my review on Steam at least.