Guard dog is most effective at taking out weak enemies with 1-2 health that deal 1 damage. This allows it to maximize its (guaranteed damage) triggered ability and save a few actions.

Take this example in a Roland deck:

1. Weak enemy (1HP) engages Roland in a location with clues.
2. Roland has guard dog in play, and decides to draw a card (or just walk around like a boss).
3. This triggers an attack of opportunity (AoO), and damage is assigned to guard dog.
4. Guard dog triggers and the enemy is defeated.
5. Roland's ability triggers, and you discover a clue.

Effectively, you've killed an enemy and discovered a clue while using an action doing something else entirely.

Clarifications

-Timing structure (for the above example): trigger action is declared (i.e. move) -> AoO triggers -> damage is assigned (not dealt) to guard dog, triggering its ability -> enemy is defeated -> Roland ability triggers > damage is dealt to guard dog -> trigger action is resolved (move).

-If guard dog has 1HP remaining, it can be assigned both lethal damage and horror (1 damage + 1 horror) from an attack.

Honestly, I've not used Guard Dog a lot, but it seems to me that it's the Guardian ally for non-guardians. It can efficiently do 3 damage over time, for a reasonble cost, and it's quite nifty being able to invoke an attack of opportunity, soak it up and kill off an enemy.

However, let's face it, if you're a guardian, you probably just want to beat things - so Beat Cop is a more natural fit. And if you've got access to guardian level 1 cards, you could upgrade to Brother Xavier, who offers more, and still does 2 damage. He's better in every way.

So this leaves the place that Guard Dog shines as being with investigators with poor/moderate strength, and access to guardian level zero only. That's pretty much Jim, Rex, and Pete, and the latter two have better allies to take priority.

With Jim, though, Guard dog is pretty good, and it's health/sanity balance nicely compliments Jim's, and gives Jim a good way to do a little damage when he needs to.

Under the 'Asset Card' section of the rules it states if an asset card has health and/or sanity the investigator may assign some, or all, damage to it. This means if the investigator has other cards to soak damage, or is willing to take some damage themselves, the guard dog could do up to 3 damage to attacking enemies.

Be aware that most cards that boost damage either require 'Fight' or an attack, these will not boost the damage of guard dog.