I like to use really smart "weak" monsters. The Kobold Napoleon or the Goblin Alexander is what I like. They know that their people are weak, so they try to out-tactic and out-strategize enemies.
Then, to keep things fun, I throw in an old-fashioned "really big impressive nasty thing" once in a while so the PCs can wade into a hard-fought slugfest from time to time--in a very public way, with enormous crowds cheering them afterwards.
As PCs become more powerful I also use situations where all the power is less relevant and useful, situations where they have to deal with protocols and social constraints. Yes, you are powerful enough to tear down Lörd Vïlëbäñë's castle to the last stone, slaughter his Death Impalement Guards and julienne cut his foul corpse. Unfortunately, he's also the third cousin, twice removed, of the High Lama, whose entire family is considered sacred and doing violence to them will force your beloved king to (weeping all the time) outlaw you, sieze your lands, chattels, properties, and goods, and offer them to whomever fries you up with an apple in your mouth.
The PCs will still need their power to survive the high-octane goons that Lörd Vïlëbäñë hires, induces, or makes foul pacts with, but the straight-in approach won't solve the problem. They've got to get the bad guy to trip himself up.
Another similar trick I like is the horribly annoying underling. Some jealous martinet who holds a vital political or religious position takes a dislike to the PCs. He's on "their side", at least officially. Even if the authorities would love to have him eliminated, they can't be seen as to be involved and would be forced to take severe measures against anybody caught plotting against the little so-and-so, since such plotting would be seen as "treason".
And if I want to pull out the big guns, I recruit the Charlton Heston in my mind and have a Cardinal Richelieu (based on both the Salkind movies and the Dumas books). He really IS on the same "side" as the PCs (or at least is loyal to some of the same causes), bears them no enmity, but he also has his own plans, is quite amoral, and weeps for nothing, not even his own defeats. Of course, that may end up with the PCs working for him, since he tries to recruit the best to his cause.
I'm the kind of DM who will have a "wizard's tower" with traps in it like this: The PCs get in without wearing the wizard's amulet, so they are hit with an unpleasant but far from lethal security device. Eventually, they get to a corridor with visible scorch marks on the walls and a hint of acrid odor. As they approach the hall, they either step on a flagstone that slightly sinks with an audible "click" and the sound of mechanisms or they find a flagstone that looks like some kind of trigger. It's right at the beginning of the hall. There is one surefire safe way down the hall--walk straight down the middle, making sure to step on the very large flagstone, which disarms the automatically lethal traps. Stay in the middle of the hall and do not touch the walls. Killed a PC with that one. To make matters worse, the players knew that the wizard in question was absolutely gaga for Faerie lore, and all Faerie lore agrees that, no matter what, you should not leave the path...
