This is indeed a tough choice. Lets see. I will not pick more than one game per franchise for this list to make it easier to narrow it down and to not have just a list that has 3 Final Fantasy games in it
1. Final Fantasy X (2001)
FF X has been my most favorite game for more than 11 years and I dont see that changing anytime soon. Never before did a game touch and move me to tears like this, never before (and never again) did I feel so much connected with heart and soul to a game and never again did I have such a huge emotionally overwhelming experience. I love nearly every single thing in this game. The world, the characters, the CTB battle system, the summoning system, the sphere Board-system, the music, story, the optional challenges. the graphics were mindblowing 10 years ago and still look really great (and will look absolutely stunning in the Remaster) and the orchestral version of the theme song "To Zanarkand" is my most favorite piece of videogame music ever created. This will always be the ultimate videogame to me.
2. Resident Evil (2002)
I have been a die hard RE fan since playing RE 2 back in 1998 but the absolute greatest jewel of the series was the Remake of the original RE for Nintendo Gamecube in 2002. It surpasses the original in every way. The graphics are near photorealistic and are still mindblowingly gorgeous. The sound and entire atmosphere of the game is absolutely unparelleled when it comes to horror games, the environments perfectly mirror the original but make everything bigger and grander. the addition of defense weapons and features such as the 180 degree quick turn (that were not featured in the original) was very good and the additional Lisa Trevor subplot or the addition of the scary as hell Crimson Head zombies only added to the intensity. Many of the bossfights like Neptune or Yawn were also much more scary and memorable and they added more story to it. However Capcom retained everything that made the original great in the first place as well and thus not only created the best RE game of the classic gameplay style that would even surpass the beloved Resident Evil 2, they also created pretty much the greatest horror game of all time. The only downside here is that the game remains Nintendo-exclusive until this day.
3. God of War III (2010)
While I initially was sceptical of the GoW - Series (being a die hard Devil May Cry fan instead back in 2010), once I started playing it, I instantly fell in love with it and today it is by far my most favorite action-series of all time. With God of War III, Santa Monica Studios reached the absolute pinnacle of this franchise. The game is a giant ultraepic , gory action-blockbuster that can rival a 200 Million Hollywood blockbuster easily. It is one of the most stunning and gorgeous games of all time with action and epic bossfights that can only be described as absolutely legendary. Surprisingly enough the game has also a lot of heart towards the end and delivers a heartfelt and more than satisfying conclusion to the story of the tormented Kratos who in his final act becomes a selfless hero and finally finds peace. This game is pretty much everything you could ever want from an action game. Its epic, its mindblowingly beautiful, its gory as hell and has a great story. Most of all its just so damn fun. Though its strongly advised to play Gow I and II before playing III since they really are very closely connected in one big saga. Kratos´Saga is in my opinion an absolute must-have for everyone who owns a PS3 and is even remotely interested in action, blood and myth.
4. Batman: Arkham City (2011)
Usually games based on Superheroes suck badly and dont do the source material (or the fans) justice. Rocksteadys Batman: Arkham games are the mindblowing exception. In Fact they might be some of the best games ever made and both received universal praise and acclaim for a very good reason. They are both very faithful to the comic universe of Batman, adapting several characters and storylines straight from the comics so if you ever wanted to really be in that universe as a fan, this is the game for it. The mix of spectacular and challenging action and Batmans famous detective work, gadgets and predator-skills (taking out enemies silently from above, behind or below) is extremely addictive. Add to that an awesome story and absolutely phenomenal voice actors (most of all Kevin Conroy as Batman and Mark Hamill as the Joker who both voiced these characters in the animated series as well) and a truly faithful setting as well as perfectly fluid and intuitive controls and you get some of the greatest games ever made.
Arkham City surpasses its predecessor Arkham: Asylum with an open world where you can freely explore every corner and rooftop of a large portion of Gotham City (that has been turned into the superprison Arkham City), much more gadgets, improved controls , twice as many Secrets to find (over 400), several additional sidequests that add characters that dont appear in the main story (such as Bane, Deadshot, Hush, Victor Zasz or the Riddler), many more of the most famous Batman villains that were not in the first game (such as Two-Face, Penguin, Ras al Ghul, Hugo Strange, Solomon Grundy or Mister Freeze), the addition of Catwoman, Robin and Nightwing as playable characters (Catwoman in the main story, Robin in a DLC episode and all three of them in Challenge maps) and much more.
Batman: Arkham City is one of the most perfect games ever made. Its a MUST for a superhero, comic book or Batman fan but its a great game for everyone else to enjoy and get into the world of Batman as well. The successor Batman: Arkham Origins will be out on October 25 and is actually a prequel to the previous two Batman games with new features, characters (including Deathstroke and Black Mask), an open world twice the size of Arkham City and new voice actors. Cant wait!!
5. Tomb Raider Trilogy (2006 - 2008)
The Tomb Raider Series and particularly the character of Lara Croft is something that I have been a fan of since 1998 and it was in fact the very first gaming series I became a fan of. While the 90s TR games (especially TR II) were legendary, I think when Crystal Dynamics took over from developer Core Design and rebooted the entire series and character with Tomb Raider: Legend in 2006 the series really got better than ever and was also much more fun and awe-inspiring than ever. This was followed up with a Remake of the original TR called Tomb Raider: Anniversary in 2007 which not only surpassed the original TR in every way but also served as a prequel for the rebooted continuity. The trilogy and Laras story were then concluded in the next gen Tomb Raider: Underworld, which to me is still the most gorgeous TR to date. Crystal then released the trilogy as HD remaster in a nice package for Playstation 3 in 2012, complete with trophy support for all three games.
While Tomb Raider has been rebooted into an entirely different game in 2013, to me its Crystals TR Trilogy which is the pinnacle of the series. It retains the traditional aspects of the 90s TRs and of Laras appearance and character while also updating everything with intuitive and fluid controls, more emphasis on characters and storyline and more interaction and of course beautiful graphics. While 2013 reboot is a very well crafted and received action adventure, it really lacks the feeling of a more traditional TR game for me as a fan of the series since 1998, while Crystals TR Trilogy really is the perfect blend of familiar tradition and modern redesign. Lara Croft is such an amazing, beautiful and sophisticated icon of the gaming world and these three games are definitely to me the best incarnation of the character and her story. And three games I have fun just playing over and over again.