The Elder Scrolls V: Skyrim is the fifth installment in the Elder Scrolls series, which is a fantasy action role playing game set in an open-world. Players control their character in a first person view and explore an expansive map through open choices.
Pro Huge variety of mods
Bethesda Softworks has upheld a tradition of releasing their internal content-creation tools to the public since Morrowind (2002). Many modders transition to new Bethesda games as they are released, bringing their experience with them and helping newcomers through forums and wikis. As a result, Skyrim's mod selection is outstanding in both variety and quality.
Pro Unrestrictive skill-based RPG system
Skyrim has no concept of character classes, and there are no restrictions on what equipment or magic a given character can use or learn. A character's capabilities are defined by skills (e.g. heavy armor, marksman, enchantment) which automatically improve as they are used. Levels are gained by increasing skills, and each level grants one perk -- a passive, secondary effect which further enhances a particular skill -- and increases an attribute of your choice (Magicka, Stamina or Health).
Pro The longest-running RPG-FPS franchise, with world lore rivaling classic fantasy literature
The Elder Scrolls series stretches back 20 years and has always focused on providing a rich world to explore. Skyrim inherits the stories and world-building of over half a dozen previous games.
Pro Moral choices that can affect gameplay
Things like stealing (and getting caught), fighting or killing in towns will change how the game plays as now those people or towns will be angry with the player, which makes things much more difficult. There are also many moral choices in game such as if one should betray the person who gave then their quest by keeping the treasure they were hired to return. All of these things will change how the game plays and how NPC's react to the character making for a simulated real world of consequences.
Pro Deep lore rivaling classic fantasy literature
Skyrim inherits the stories and world-building of The Elder Scrolls series, which stretches back 20 years. It has numerous stories surrounding the various races (orcs, elves, lizardmen, demons, etc.), mythical beasts, gods, cataclysmic events, parallel worlds, and just about any fantasy trope you could think off. What's even better you can read the lore in books found in-game, allowing you to immerse yourself for countless hours.
Pro Total freedom in how you choose to play through the world's different factions
You can set off to any of Skyrim's different towns and discover new storylines from interesting factions that flesh out the world and the lore, with great characters and their own absorbing narratives to get lost in. There are a good number of these factions, like the scholars at the snowy College of Winterhold, the secretive assassins of the Dark Brotherhood, or the cohort of rogues and bandits of the Thieves Guild. After picking whichever faction you want to learn more about, you can eventually become a Master of the guild and learn new skills for your character. Playing through each of their individual stories lets you really feel like a member of the faction you choose, like with how the Thieves Guild sends you on missions to pick locks and steal valuables without getting caught by the guards.
And if you only get through some of the faction's story and decide you don't enjoy it, you can easily go find another one and play through that one instead. There are no limits on how you play through the plot, with Skyrim giving you the flexibility to pick up stories, set them down, and come back to them whenever you feel like it.
Pro Massive sandbox to explore at your own pace
The in-game map is absolutely gigantic. There are so many places to go and so much to do in the world, easily giving you hundreds of hours of content.
Exploring the wide range of environments, from the snowy mountains to the richly-detailed towns and cities is such a joy because of how lush and beautiful everything is. Wandering around often surprises you with new side quests to find off the beaten path, with new characters to meet and history to learn about in whichever area you find yourself in. You can get into all sorts of battles with powerful enemies or stumble into hidden dungeons with awesome loot at the end. Or you can sneak around towns at night stealing peoples' stuff while they're asleep to sell everything off for money. And there's just a ton of other intriguing secrets and fun diversions to discover as you adventure throughout the world.
Con Forgetful NPCs can break immersion
After completing certain story quests NPCs get new lines added to their dialogue based on your decisions. Sometimes the NPCs might become forgetful and return to their default dialogue, which can break immersion, especially if they talk about an event that's been long resolved.
Con Combat is too simple
Fights within the game don't have very many options. "Headshots" don't matter, and most combat options in the game are poorly balanced.
Doesn't really matter if you go mace, sword or axe, fire, ice or lightning, or even two handed vs dual wielding. The options mostly add flavor to your character and little else.
Despite the fact that you might have ranged attacks, dragons are impossible to hit while in the air, so you end up fighting them similarly to a melee character.
"Twincasting" the first healing spell is actually worse than just casting it once in each hand.
Illusion magic becomes useless at later levels, since the spells don't do anything if the enemy is too high level and enemies scale to your level.
Enemies are too stupid to make hiding a bad thing.
The worst one is leveling as an Alteration mage, which gives you access to the Dragonskin spell, granting maximum armor for 30 seconds and has a 5 second cast time. Or you could just go Heavy Armor, level that up (so it weighs nothing) and have maximum armor ALWAYS without ever having to cast an Alteration spell before combat ever again.
Combat comes down to how you leveled, not how you play.
Con Immersion can be broken due to game limitations
While the game offers players many choices some of these choices are not reflected in the game accurately. There are instances where NPCs should know who your character is or what classes they belong to but due to the limitations of the tech used in the game it is unable to "remember" these things and so NPC text will often break immersion in the game by saying the wrong things.
Con Buggy and crash prone
Skyrim, like all Bethesda in house game engines (GameBryo) is buggy and prone to crashing. Non modded games have plenty of issues, but to then add mods on top is just asking for a crash or corrupt game save.
There are still many community mods for Skyrim that try to make the game more stable by addressing memory issues and general buggynes. While the game is not as buggy as it was upon release, there are still many people that have issues with the game crashing on boot or just randomly which is why these mods are still widely used and still very relevant.