My druid's sole "permanent" animal companion is a mangy cat. He tends to spend more time in cities than the typical druid, so a cat is much less problematic than, say, a dire bear. In my case, I see my animal companion as a
companion, not a servant.
Of course, having just hit 9th level, I do plan on Awakening the cat as soon as I have the chance. Once he has some decent hit points and the smarts to protect them, I may start using him as a scout.
As far as our monkey-loving druid (and I'll admit I considered a monkey myself, but couldn't justify it with a character originating in Silverymoon from FR), there's a ritual that druids can perform in MotW (if you use that splatbook, its on page 37) that lets you increase the HD of an animal companion by one for 200 xp. Since monkeys can advance up to 3 HD (growing to Medium size at that point), giving it more hit points and skill points (for an even better Hide or Climb), or even a few appropriate cross-class skills; Open Lock is probably beyond a 2 Int animal, but consider Perform (dancing in the street for coins), Pick Pocket, Tumble, and Move Silently are options. Let's not forget the use of other spells and magic items (there are a few animal-specific items in MotW, and given the monkey's vaguely humanoid form, you could be really nice and allow the use of PC items like rings).
And of course, if she makes it to fifth-level spells, then Awaken opens up a range of possibilities. Depending on your feelings about this as a GM, perhaps even allowing the monkey to earn XP like a follower and gain class levels (This is Bubbles, the Barbarian...)
But you originally asked for advice on an encounter that would allow the monkey to be useful. I'd start by finding out from your druid player what she wants out of her animals. If they are like my druid, then maybe they don't even want the monkey to be "useful" - they just want a slightly exotic pet. If, however, she has been complaining that she never gets to use her animal companion, then the previous suggestions are good. The monkey's advantage over most animals is the possession of humanlike hands (and possibly a prehensile tail, depending on the species) and a greater Int than most animals. The strict rules for using animal companions doesn't reflect this (the monkey could learn six tricks), so it might require a bit of stretching on your part. I wouldn't go nuts (suddenly the monkey can disarm a needle trap and open a multiple-tumbler combination lock).
Remember the Nazi Monkey (tm) from Raiders of the Lost Ark? There's an example of a useful animal (though I doubt the druid will consent to letting the monkey taste-test the party's food to check for poison) whose behaviors fall outside the "six-trick" limits of 3E. There may be other movie examples, but I'm failing to think of them at this early hour - the only one that comes to mind is "Outbreak", but I don't know if 'spread plague' would be an acceptable animal trick in your campaign...
Edited: realized that the player was identified as female, so took out the "he or she"s - also added one or two more bits of advice.