Note that you can easily obtain all of these armors regardless so feel free to experiment! Mix and match as you please.
Keep in mind that all sets listed in here should be upgraded as much as possible (when/if possible). Obviously some won't be upgradeable, such as the Havel Armor set. Also, this article is written in the beginning of 2013 -- so it's for the latest patch 1.07 AND applies to those with the Artorias of the Abyss DLC.
These work great for player vs player (PVP) (invaders) and player versus everyone (PVE). This includes against bosses and normal enemies too.
Dark Souls: Best Heavy Armor
These work best when using the HAVEL RING to lighten your load (you should also have more endurance). This takes up a ring slot unfortunately, but it is worth it. The second ring slot can be anything, such as the WOLF RING which adds 40 extra poise. These sets will make you a great tanking machine! Note that you'll need more strength than with other sets, so this is great for a strength build, faith & strength build, pyromancy + strength build, or int / intelligence / hybrid sorcery build. Alternatively, it works also for those who have a strength & quality / dexterity (dex) build too, which gives you great weapon flexibility.
Havel's Armor Set - This will make you significantly stronger. It has the best poise, curse resistance, and magic resistance of all heavy armor sets in the game. Plus good over all elemental resistance. If you don't need to be fast, then this is the one to get. You will be a TANK (or as close to a tank as you can get in this game).
Smough's Armor Set - Some people go this route instead of the Havel route. This has the great physical defense, great fire defense, lightning defense, and bleed defense.
Black Iron Armor - When upgraded all the way has the best fire defense and best poison resistance -- so great for fire & poison levels and against bosses or enemies that use fire or poison). It weighs less than the Havel armor set AND provides a lot of poise and defense. This is a great choice.
Giant Armor Set - This set has the best physical defense of them all when upgraded.
Some people may recommend the Iron Golem Set, but you won't get that from me!
Dark Souls: Best Medium Armor
These are good for PVP, as it helps you not get too weighed down, but adds defense still and poise.
Elite Knight Armor Set - Easily obtainable, this is one of the most popular medium armors to use.
Dark Set - It's cool, it's evil looking, and it has good stats! Upgrade it to +5 and it becomes even better.
Paladin Set - This is found in Gravelord Nito's chamber.
Knight Set - It weighs less than the EK set above, but has the same poise.
Hybrid - Using Havel's leggings + Gauntlets with your choice of helmet and armor works well for giving you extra poise.
Some people like the Catarina Set, but I haven't listed it. It's pretty silly looking though so definitely worth using for fun!
Dark Souls: Best Light Armor
For maximum mobility, light armor is the way to go. It gives good resistance usually too, but it is missing one important aspect. POISE! Because of this, you must make sure to dodge or you will be in trouble. I recommend using a WOLF RING with this build.
Gold-Hemmed Black Set - This is one of the best armor sets in the whole game! It's very light weight and has fantastic resistance (especially towards fire). It can be used for the whole game after obtaining it. It has the 2nd best poison resistance in the whole game (the fully upgraded Painting Guardian Set surpasses it here [thanks Painted]), which is great in swamp levels and when dealing with poisonous enemies. It can't be upgraded / reinforced though.
Crimson Set - Light weight and helps. I'd still go with the gold-hemmed black set instead though.
Xanthous Set - Talk about some weird looking armor (at least the helm ~ the Xanthous Crown). It works well for light armor though.
Mix & Match Gear
If you want to mix and match some parts of your set, here's some good options.
Smough's Gauntlets - Have the best lightning resistance of all gauntlets.
Wolf Ring - Not an armor, but this adds 40 poise to your character. GREAT for tanking while still dishing out damage!
Greatshield of Artorias - Best shield in game for poise. So if you want high poise, this is the way to go. Otherwise, I'd recommend the Black Iron Shield.