The information was a little hard to come by so I figured I'd write something up. At time of writing, v6.2 update, v7.0 is the latest firmware available.
The main reason why most people would want any firmware between 4.1-4.5 is to use the Gateway card. The Gateway card lets you bypass the region locks which make it incredibly difficult to get the exact games you want.
If you're looking for a "PS3 way" to upgrade (download a specific firmware and upgrade it via storage) then you're outta luck. The 3DS requires you to log online and get the latest firmware via the eStore. There's no choices there, only the latest and greatest patches.
Upgrading
In order to upgrade to a specific version of firmware, you have to buy a game which was made during that time when the firmware was "latest".
Note: This only works for upgrading. It is not possible to downgrade using this method!
To check which firmware each game is running, check out http://3ds.essh.co/. It has a very nice filter which tells you exactly which firmware the game is using (scroll to the far right). Sort it by firmware so it's easier to find the right region.
Once you've picked the game you want to buy, run it. The game will check your firmware and if your firmware is older than the one it came with, you'll be asked to upgrade to the firmware included with the game.
As shown here.
Game titles by version
Just in case the site goes down, there is another list at EurAsia wiki.
Firmwares have a letter at the end signifying the region it was intended for. U or USA, E for Europe, J for Japan. I'm not quite sure what firmwares ending with T and K stand for but I assume it's Taiwan and Korea.
I've sorted this list by firmware and region to make things easier.
Firmware v4.5
4.5.0U | Shin Megami Tensei IV |
4.5.0E | Animal Crossing - New Leaf |
4.5.0E | Animal Hospital |
4.5.0E | Donkey Kong Country Returns 3D |
4.5.0E | Fire Emblem - Awakening |
4.5.0E | Games Festival 1 |
4.5.0E | LEGO City Undercover - The Chase Begins |
4.5.0E | LEGO Legends of Chima - Lavals Journey |
4.5.0E | Luigi's Mansion 2 |
4.5.0E | Pokémon Mystery Dungeon - Gates to Infinity |
4.5.0J | Luigis Mansion 2 |
4.5.0U | Donkey Kong Country Returns 3D |
4.5.0U | LEGO City Undercover - The Chase Begins |
4.5.0U | Luigis Mansion - Dark Moon |
4.5.0U | Pokemon Mystery Dungeon - Gates to Infinity |
4.5.0U | Turbo - Super Stunt Squad |
Firmware v4.4
4.4.0E | Around the World with Hello Kitty and Friends |
4.4.0E | Castlevania Lords of Shadow - Mirror of Fate |
4.4.0E | Croods, The - Prehistoric Party! |
4.4.0E | Fast & Furious - Showdown |
4.4.0E | Jewel Quest Mysteries 3 - The Seventh Gate |
4.4.0E | Monster High - Skultimate Roller Maze |
4.4.0E | Monster Hunter 3 Ultimate |
4.4.0E | My Riding Stables 3D - Jumping for the Team |
4.4.0E | Paper Mario - Sticker Star |
4.4.0E | Project X Zone |
4.4.0E | Secrets of the Titanic |
4.4.0E | Sonic & All-Stars Racing Transformed |
4.4.0E | Viking Invasion 2: Tower Defense |
4.4.0E | Zero Escape - Virtues Last Reward |
4.4.0J | Castlevania Lords of Shadow - Mirror of Fate |
4.4.0J | Dragon Quest VII - Eden no Senshitachi |
4.4.0J | Layton Kyouju to Choubunmei A no Isan |
4.4.0J | Pokemon Fushigi no Dungeon - Magnagate to Mugendai no Meikyuu |
4.4.0J | Super Robot Taisen UX |
4.4.0T | Mario Tennis Open |
4.4.0T | New Super Mario Brothers 2 |
4.4.0T | Shin Megami Tensei IV |
4.4.0U | Brain Age - Concentration Training |
4.4.0U | Castlevania Lords of Shadow - Mirror of Fate |
4.4.0U | Etrian Odyssey IV - Legends of the Titan |
4.4.0U | Fire Emblem - Awakening |
4.4.0U | Mario Tennis Open |
4.4.0U | Monster Hunter 3 Ultimate |
4.4.0U | Naruto Powerful Shippuden |
4.4.0U | Shin Megami Tensei - Devil Summoner - Soul Hackers |
Firmware v4.3
4.3.0U | Art Academy - Lessons for Everyone |
4.3.0E | Angry Birds Trilogy |
4.3.0E | Ben 10 - Omniverse |
4.3.0E | El Profesor Layton y la Máscara de los Prodigios |
4.3.0E | Il Layton e la maschera dei Miracoli |
4.3.0E | Naruto Powerful Shippuden |
4.3.0E | Pro Evolution Soccer 2013 3D |
4.3.0E | Professeur Layton et le Masque des Miracles |
4.3.0E | Professor Layton und die Maske der Wunder |
4.3.0E | Puzzler Brain Games |
4.3.0E | Rise of the Guardians |
4.3.0E | Survivor 3D - The Ultimate Adventure |
4.3.0J | Fantasy Life |
4.3.0J | Inazuma Eleven Go 2 - Chrono Stone - Neppuu |
4.3.0J | Tobidase Doubutsu no Mori |
4.3.0T | Naruto SD Powerful Shippuden |
4.3.0U | Hotel Transylvania |
4.3.0U | Paper Mario Sticker Star |
4.3.0U | Pro Evolution Soccer 2013 3D |
4.3.0U | Professor Layton and the Miracle Mask |
4.3.0U | Style Savvy - Trendsetters |
Firmware v4.2
4.2.0T | The Legend of Zelda - Ocarina of Time 3D |
4.2.0T | Biohazard Revelations |
Firmware v4.1
4.1.0U | Lalaloopsy Carnival of Friends |
4.1.0E | Bowling Bonanza 3D |
4.1.0E | Disney Epic Mickey - Power of Illusion |
4.1.0E | Disney Princess: My Fairytale Adventure |
4.1.0E | Freakyforms Deluxe |
4.1.0E | Hotel Transylvania |
4.1.0E | Imagine - Fashion World 3D |
4.1.0E | Jewel Master - Atlantis 3D |
4.1.0E | LEGO The Lord of the Rings |
4.1.0E | LEGO The Lord of the Rings |
4.1.0E | New Art Academy |
4.1.0E | New Super Mario Bros. 2 |
4.1.0E | Pippi Longstocking 3D |
4.1.0E | Rabbids Rumble |
4.1.0E | Sherlock Holmes - The Mystery of the Frozen City |
4.1.0E | Shin Megami Tensei - Devil Survivor Overclocked |
4.1.0E | Spy Hunter |
4.1.0E | Transformers Prime - The Game |
4.1.0J | AKB48+Me |
4.1.0J | Bravely Default - Flying Fairy |
4.1.0J | E.X. Troopers |
4.1.0J | Project X Zone |
4.1.0J | Sengoku Musou Chronicle 2nd |
4.1.0J | Tohoku Daigaku Karei Igaku Kenkyuusho - Kawashima Ryuuta Kyouju Kanshuu - Monosugoku Nou wo Kitaeru 5-Funkan no Oni Training |
4.1.0T | Nintendogs + Cats - French Bulldog and New Friends |
4.1.0T | Nintendogs + Cats - Shiba and New Friends |
4.1.0T | Nintendogs + Cats - Toy Poodle & New Friends |
4.1.0T | Star Fox 64 3D |
4.1.0U | Adventure Time - Hey Ice King! Whyd You Steal Our Garbage?! |
4.1.0U | Code of Princess |
4.1.0U | Disney Epic Mickey - The Power of Illusion |
4.1.0U | Disney Princess - My Fairytale Adventure |
4.1.0U | Finding Nemo - Escape to the Big Blue |
4.1.0U | Harvest Moon 3D - A New Beginning |
4.1.0U | Imagine - Fashion Life |
4.1.0U | LEGO The Lord of the Rings |
4.1.0U | Myst |
4.1.0U | New Super Mario Bros 2 |
4.1.0U | Rabbids Rumble |
4.1.0U | Scribblenauts Unlimited |
4.1.0U | Skylanders Giants |
4.1.0U | The Trash Pack |
4.1.0U | Wipeout 3 |
4.1.0U | Wreck-It Ralph |
4.1.0U | Zero Escape - Virtues Last Reward |