I think there's a strong impetus toward using monsters primarily as combat opponents, simply because they're statted up primarily for combat purposes. The stats tell us that a giant rat CAN attack as a 1/2 HD monster and do 1-3 points of damage per hit, plus possible disease. In and of itself, however, that doesn't really tell us any more about what a giant rat WILL do in an encounter than knowing that a magic-user can attack with his dagger for 1-4 points of damage tells us what he will do. Just as the magic-user has all sorts of options open to him other than rushing into battle with his dagger (which most of the time would end badly for him,) the giant rat has options other than rushing into battle (which most of the time would end badly for it.) A creature's stats are not the sum total of its abilities, only those which pertain to direct physical combat.
Think about all the abilities and actions available to a particular monster, not just those listed in its stats. Then think of what it's likely to do, not just what it can do. If the monster has a real world analog or counterpart, draw on that for clues to its abilities and behavior?
- What are its physical capabilities? Can it do things that are too mundane to merit mentioning in its stats or description but which might be of use in certain situations?
- How intelligent is it and what does it know, or know how to do? What are its skills?
- What is its general disposition? Is it aggressive, timid, curious, playful, territorial...?
- Does it have any behavioral quirks or idiosyncrasies?
- Does it have any particularly strong fears?
- Does it have a "berserk button" that will enrage it and provoke an attack?
- Is there something that pacifies it easily?
- What does it currently want or need? Does it have long-term plans, and if so, what are they and how is it pursuing them?
- How long has it been where the characters encounter it? Why has it chosen to be there? How does that place serve its current needs? Has it altered the place to be more suitable?
Instead of rehashing the giant rat, I'm going to apply this to giant beetles. I'll take the giant fire beetle specifically:
Real world beetles can crawl up walls, fly, and squeeze into tight spaces. Perhaps giant fire beetles are too heavy to really soar, but I think they should be able to hover for a round or two and make flying hops within the limits of their movement rate, sort of like a chicken. They can see into the ultraviolet spectrum, and sense movement and vibrations with their antennae. They have some pretty powerful mandibles that are probably good for other things besides biting for 2d4 damage, such as gnawing and burrowing. They have bioluminescent glands; the function is not specified, so I'll just invent something plausible: they're used to identify other members of the species and to attract mates. They're pretty much non-intelligent, acting only on instinct. The rule book doesn't say what they eat, but it doesn't seem like a predator, so it's likely a scavenger. Its morale is 7, a little unsteady, so it's not terribly aggressive. The book states that it's nocturnal, so it's a pretty safe bet that it doesn't like really bright light and will probably flee from it.
Beetles aren't much for long-term planning. A fire beetle probably has no more pressing needs than feeding and reproducing. It's likely to be encountered in places that serve those needs, and it will probably excavate a lair for itself if possible.
When encountered, the fire beetle is probably not going to attack the PCs, either for territorial reasons or for food. It is likely to be attracted to lights carried by the party, though. It might see them as potential mates and try to court them, as potential rivals and attack them, or just as fellow fire beetles and blunder around them like moths around a flame, depending on the reaction roll. In any case, there's a possibility that they might knock light sources out of characters' hands. As scavengers, they might also come around while the PCs are resting and use those powerful mandibles to tear open packs in search of food.
How about another example? Let's take the lowly kobold.
Kobolds can do pretty much anything a typical humanoid can do. They can walk, crawl, run, jump, climb, probably swim, grasp objects, use tools... They're small, which means they can go places that humans can't. They have infravision to 90'. Being underground-dwellers, they probably know a thing or two about tunneling and mining, and they probably aren't claustrophobic. Tight passages don't faze them.
The book says that kobolds prefer to attack by ambush, and their morale is 6. They're rather cowardly, but also malicious and mean - not above vicious murder if they can get away with it, but probably a lot more inclined to thievery and malevolent mischief that doesn't put them toe-to-toe with big dangerous adventurers and their big dangerous swords. They're intelligent (according to the Mentzer-edition Master Set, an average of 9) and probably quite cunning.
Kobolds are probably concerned mostly with staying alive, which they manage by avoiding direct confrontations with more powerful creatures (that's almost all of them) and by opportunistically pilfering food and supplies. They also have a mean sense of humor, and enjoy rapping on walls and making strange noises to lure parties into traps or other hazards, and especially delight in getting adventuring parties hopelessly lost in the dungeon. (Kobolds themselves never become lost in underground settings.)
Kobolds prefer small spaces, which are inaccessible to larger adversaries, but they also like to be adjacent to bigger spaces where they can bedevil bigger folk. If they've lived in the area long enough, it's likely to be honeycombed with kobold tunnels and crawl-ways in the "dead spaces" of walls, floors, and ceilings, which provide quick and stealthy avenues of access and retreat to and from many areas of the dungeon. Their preferred tactic is to pop out, grab whatever they can, and disappear. Inflicting physical harm is not their primary objective, though it's certainly a nice perk if it can be managed without too much risk. They will seldom openly engage a foe, but are not above a sudden attack on a sleeping, weakened, or otherwise unprepared party.
Play around with individual creatures' wants and motives to keep players on their toes. A particular hill giant could be lonely and want companionship more than a fight. He'll talk the party's ears off if they let him, and if they aren't careful, he might take a fancy to one of them. ("I will love him and squeeze him and call him George!") An owlbear might have developed a taste for horseflesh, and ignore the PCs while it mauls their mounts. A mountain lion might shadow the party for days out of curiosity, but make them very nervous about taking off their armor and sleeping. A troll might be more interested in showing PCs how strong he is, and letting them flee in terror back to the village to tell everyone how mighty he is, than in killing and eating them. A medusa might fancy herself an artist, and promise to let the adventurers go un-petrified if they can bring her a more beautiful or interesting subject to turn to stone.
Most monsters aren't just hostile kill-bots bent on destroying anything that crosses their paths. Players are encouraged to achieve their goals of exploration and gathering treasure by creative means, minimizing risk and entering into combat only as a last resort, and monsters often should be played the same way. A monster doesn't necessarily want a fight; it wants food, or treasure, or find a mate, or get these pesky intruders out of its lair. If its abilities, intelligence, and temperament allow it to do whatever it wants to do without risking its life, it's a good bet that it will choose that way. Playing at least some of the monsters this way makes the ones that really are aggressive and belligerent by nature stand out more.