Dungeons and Dragons 3.5e
This is considered the daddy of the games. When Wizards of the Coast took over the rights to the Dungeons and Dragons game they gave is a good shake and sorted out many of the games foibles and quirks. They took the old staple (many of the people I began gaming with started out with AD&D and had moved to AD&D 2nd Edition over time) and re-launched it.
Originally the D&D 3.0 system was a great improvement, but it became better when it was given a makeover once again. The game system still suffers from the weaknesses of D&D, most notably the simplicity of of the combat system and lack of core character options, but it is expanded to cope with character skills properly, and the magic system is simple and strong as it has always been.
Character Classes
All the old favourites were kept that had been there in the original AD&D game. Barbarians, Bards, Monks and Rangers had all survived. And the Fighter class came back, it had morphed into a 'Warrior' class in 2.0, but had been restored as the game was ironed flat. Also returning was the Druid class - in 2.0 it had become part of the cleric class.
These changes were good, even if the Thief was still a Rogue, and the Assassin was still missing. The introduction of a core and flat set of skills and feats made the classes more flexible and meant that players could now take their PC's in more custom directions. These improvements gave the players a chance to become better in some areas by sacrificing others.
Magic
D&D has always been a 'spell' based magic game, those that can use them have a list of available spells, with two distinct approaches - wizards and clerics can pick their spells at 'learn' time and so get more available and more to pick from while sorcerers get a smaller list but get to pick their spells at cast time. This is a great compromise and works well. It still encourages the approach of fighting on until the cleric is out of healing and then retreating to rest, which is a sound tactic in many games, not just D&D derived ones.
Weapons and Armour
While the game still cannot spell Armour properly, it has a big enough array of weaponry and defences to cover most characters needs. Feats are now required to use weapons and armour by category (although some classes get some for free, which is a sensible rule). The bonuses for each are also levelled - there is no THACO table in 3.5 (something that made the game maths in AD&D 2 and earlier a bit tricky) and no negative armour classes - here everyone is a 10 with armour and dexterity adjustments, plusses meaning better and minuses meaning worse. That's just logical. Now the AC is the base difficulty number (on a D20) to hit.
Character Progression
The chunks in character progression are still quite large. It's almost like a 2nd level character really is almost twice as good as a 1st level character. It would be nice to see a more graduated improvement, but the game is inherently built on these levels, and has been since the oldest incarnations of the game. Above 3rd level, though, things are much better. The introduction of the feats and skills has also helped enormously, not only is progression and improvement set up to allow more specialisation, it's also introduced much more variety.
Quirky Oddness
There are weaknesses in any system, but the fun ones in D&D seem to be the same as they've always been.
Character movement is discrete, i.e. one character does all their movement and acts before another does the same thing. There is no 'partial' movement, although there's nothing to stop this being added to the game if you can cope with the complexity.
Injury and death is another. It's a constant source of amusement that every character in D&D can be stabbed, burned, bludgeoned and exploded, but while they even have a single hit point left, they're absolutely fine - there is no pain and no struggle with the injuries you might have picked up. I suppose that's to help them look like the heroes they are, a bit like Bruce Willis in the various (and interchangeable) Die Hardish films.
There are lots of other bits where the rules don't quite sit right, but as it's D&D, these can be quite charming and nothing that isn't resolvable by a good DM.