I'm a big fan of the Assassin...I've been playing one in the RPGA since just a bit after GenCon. I'm only level 10 so I don't know much about Paragon (I'm planning on going with Arcane Trickster from Martial Power 2...I'm multiclassed Rogue but that's neither here nor there...none of the Assassin PPaths appeal to my kind/"I don't want to swallow peoples souls" vanishing Kenku).
It seems everyone plays their Assassin a bit differently. For me, it's all about not being seen. Even with the Stealth rules being revamped now and again, the Assassin has a lot of "weird" powers that let you hide when you usually wouldn't be able to. Shade Form lets you hide behind allies...and if a power doesn't give you out and out invisibility then often it lets you do some weird trick where you can hide even if you only have cover. Hell, at Paragon you can use Enemies as Cover, meaning you can often Hide from enemies by hiding behind Enemies. O_O (Important rule though: Just because you're invisible doesn't mean you're Hidden. Took me a while to sort that out). I can't gush about the level 10 Utility "Seeker of Shadow" enough...for at least the first 2 rounds you're invisible from the moment you roll for initiative.
Other powers that have shined:
GloomThief: It's basic but it gives you Invisibility.
InEscapable Blade: There's something fun about having a Melee +2 Reach attack that lets you stab people through walls. It also means you can hide around corners from a target and still stab them through said corner.
ShadowJack: You get to ride an enemy around the battle field and if folks miss you, they hit your newly acquired mount. Also gives you a round of Insubstantial.
Cloaking Mist lets you hide from the Blast targets hit or miss even if you only have Cover.
Obviously, my build is all about not being there when the enemies want to hurt me...when I'm not invisible and/or hidden, I'm doing something wrong. Early on I learned that the Assassin is kind of squishy. Be on the front lines, but don't let them see you. Someone else has already said it but: Stick near the Defender or, at the very least, after you stab the boss teleport behind the Ranger. Better them than you.
Other stuff: Keep in mind if you go with the Nightstalker Extra damage build option, that damage bonus applies to all your attacks, so don't be afraid to mix it up. Your shrouds and bonus damage still work fine with ranged attacks so if things are getting tough, pulling out a crossbow or something still lets you keep up the pace, though it'll lack the traditional Assassin flourish.
Finally: Check out the feat tricks the Assassin can pull off.
YOu have 2 Poison-Related feats. 1 that lets you do an extra 2 damage when you deal poison damage and another that means when you DO deal Poison Damage it ignores Immunity & Resistance. If you take the Spiderkissed Weapon that allows you to convert all the damage dealt with your weapon to Poison damage, then suddenly all your attacks do full damage to, well, everything that might resist you.
...and there you go. Ignore what you want but that's pretty much the stuff I've enjoyed with the assassin.
-Jared