These guides are those that are considered up to date with what is currently "state of the art." You should be able to pretty much follow them directly.
The Assassin FAQ
General reference to everything that relates to Assassins.
Assassin IAS Tables
Attack speeds for all attacks compared to Burst of Speed level
Shuko-jutsu: The Art of the Claw by maxicek
Everything you ever wanted to know (and much you probably didn't) about claws, including what to look for in a claw, shopping, how affixes are generated etc.
Blade Fury Analysis by Ceramic Weasel
Explores the mechanics of Blade Fury and how it's damage can be maximised.
Assassins are not the most powerful character in D2. A Lightning Fury Amazon or a Sorceress will kill much quicker than even the best built Lightning trapper. They are however probably the most versatile class in D2. Dragon Talon gives them one of the best boss killing skills. It is easy to combine at least two elements, with some of the best (or the best) crowd control skills in the game and a castable tank. They can play as pure melee or pure caster. Or a combination of all the above.
Warrior Monk Uber Trist Guide by JanusJones
If you are planning on taking on the Ubers with an assassin, this guide should be your starting point. Also includes a good analysis of all the possible kick / blade fury weapons in the game.
Sara's Rift-a-Sin PVM by Master Zap
Dragon Talon combined with the 'Rift' runeword to trigger Frozen Orbs. This guide focuses on maximising the orb damage.
The Untwinked Lightning Trapper by jrichard
A general guide on playing a Lightning Trapper through the game. It offers a number of approaches to the build and general pointers on what to look for in equipment, rather than prescribing specific items.
Kick / Trap Guide by Ilkori
Ilkori's definitive guide to Kickers, Flashdancers and Firedancers. The only guide you need for Dragon Talon with traps in PvM.
The Aggressin: Dragon Claw / Death Sentry Assassin by maxicek
A physical damage, dual claw based build without using charge ups. The guide includes variants with bespoke equipment and using Natalya's set.
A Comprehensive Guide To Phoenix Strike by maxicek and jiansonz
Covers all aspects of Phoenix Strike, including twinked and un-twinked play, hardcore and softcore. Natalya's Set Phoenix Strikers are also included.
Dragon Tail - A Build Guide by maxicek
Dragon Tail with a Tiger Strike charge up can generate huge damage, but you need to be able to harness it properly. This guide focuses on how to deal with the problem of physical and fire immunes.
Dragon Flight by JRichard
It is an old guide which focusses on using Dragon Flight as a finisher with Phoenix Strike. There are some interesting ideas in here, read in conjunction with the PS guide above.
The foundation of all current PvP assassin builds is at least one point in Mind Blast and Wake of Fire to stunlock opponents. What differs from there is how the damage is applied. It can be with traps, kicks, whirlwind or a combination of the three. But the foundation always remains the same.
LS Trapper Guide v1.0 by TienJe
The Lightning Sentry trapper is the classic PvP assassin. This definitive PvP trapper guide covers both claw/claw and weapon/shield variants.
Kicksin Guide by wizAdept
Kickers are not the easiest PvP build to master, this guide is the essential starting point on a long learning curve.
WW Ghost Assassin by TienJe
The Ghost gets its name from a heavy investment in fade for resists and damage reduction. Venom and Whirlwind from the 'Chaos' runeword to get the kill. With practice they are one of the best duellers across any class.
The Fastcast WW/Kick/Stun Assassin by SpeederlÃ¤nder
The 'SpeederlÃ¤ndersin' is best defined as a Ghost with kicks. This guide should be read as a companion to TienJe's guide above.
WW/Trapper by HappyAssassin
A combination of a Ghost with a trapper, this very versatile build has Lightning Sentry for a powerful ranged attack and Venom/Whirlwind for a dangerous short range attack.
Bow / Kick / Fire Trapper discussion
Not strictly a build guide, this is an outline for combining fire traps with kicks. Should be read alongside the Kicksin guide above.