Half-Life's weapons are quite varied, and in some cases are a little difficult to use unless you know the tricks of the trade. Many of them are better suited to certain situations (and enemies) than others.
Category 1
Crowbar
The crowbar is the first "weapon" you find. It comes in quite handy for smashing obstacles out of the way, breaking glass, opening crates, or killing headcrabs or zombies. It's not much useful for anything else, though.
Category 2: Pistols
Glock 18 Handgun
A quick but weak pistol. Sports a 17-round clip and uses 9mm ammunition, but it's not incredibly powerful. Primary fire shoots slowly but accurately (useful for taking zombies from a distance), while secondary fire shoots faster but sacrifices accuracy. If you have the High-Definition Pack installed, the pistol changes into a Beretta 92FS - it behaves exactly the same, however.
Colt Python .357 Magnum
A much more powerful handgun, capable of killing zombies and slaves with a single well-placed shot to the head. Also capable of taking out soldiers with one or two headshots. Unfortunately, it's very slow to fire, and even slower to reload. In deathmatch mode, the Python sports a lasersight which enables you to zoom in with the alternate fire key.
Category 3: Anti-Personnel Weapons
Heckler & Koch MP5/M203
A rapid-fire assault weapon that uses the same 9mm ammunition as the Glock. It's not quite as accurate, and the power is barely higher than the Glock, but the rapid fire and higher clip size (50 rounds) ensures superiority. In addition, the MP5 has an attached M203 grenade launcher - excellent for clearing groups of soldiers. Unfortunately, ammo for the grenade launcher is difficult to find.
Franchi SPAS-12 Shotgun
A pump-action assault shotgun that, while appearing powerful, is actually rather weak and slow. The primary fire shoots one of its eight shells, while secondary shoots two at once. You can carry an awful lot of ammo for this, but the weapon is too weak and slow to reload to be worth it. It'll probably be the last weapon you end up using.
Crossbow
The crossbow serves as HL's sniper weapon. It's silent, it has a scope, and it's capable of eliminating soldiers with a shot to the head. It's quite slow though (especially to reload its 5-round magazine), so make sure you're close to cover. In multiplayer, the crossbow's darts will explode on contact if you're not using the scope.
Category 4: Heavy Weapons
Rocket Propelled Grenade Launcher
A very powerful rocket launcher with a laser-guide feature. Use the secondary fire to turn the laser on and off, and the primary fire to shoot a rocket. The rocket will always try its best to follow the laser, and it does a fairly good job of it too, so shooting over obstacles is entirely possible - as is making accurate shots at Apache helicopters. You can only carry five rockets, though - and the launcher is extremely slow to reload.
Tau Cannon
The Tau Cannon is an experimental gauss rifle that has the capability to penetrate through some obstacles. It uses Cells as ammo (the max of which is 100 units), requiring 2 cells per shot. It's fairly fast, though. Secondary fire charges it for a more powerful shot. In multiplayer, the secondary fire is also used to make extremely high jumps - charge to its fullest, aim down, and release to launch yourself into the air.
Gluon Gun
The other experimental energy weapon, the Gluon fires a constant stream of Super Blue Stuff which can vaporize just about anything in a matter of seconds. It eats through cells like nothing else.
Hivehand/Hornet Gun
The severed arm of an alien Grunt, the Hivehand generates a maximum of 8 "hornets" that can be shot out at will to chase after enemies. Primary fire shoots slow "homing" hornets, while secondary shoots faster non-homing hornets. The homing pattern of the hornets is difficult to predict, but with a bit of skill, it can be used to shoot around corners at foes (but be careful in deathmatch games, as the hornets leave orange trails which can give your position away). When you're not firing it, the Hivehand regenerates its ammo supply.
Category 5: Disposable Weapons
Hand Grenades
High-explosive grenades used by the Marines to clear rooms. You can use these against them however. While they normally don't fly very far, you can throw them farther by getting a running start first.
Satchel Charges
These explosive charges are used to clear cave-ins and obstacles - however, you can also use them as manually-detonated tripmines (or makeshift grenades if you're good enough). Primary fire drops a satchel charge and switches to the remote. A second click of the primary fire detonates it. When the remote is out, you can use the secondary fire to drop more satchel charges (clicking the detonator will blow all the charges that you have thrown).
Laser Tripmines
These extremely obvious explosives make their first appearance in "We've Got Hostiles", wherein the first scientist you see ends up meeting his fate behind a fire door. When placed on a wall, the tripmine will make a loud beeping sound, then engage its laser. When this laser appears, the mine is LIVE - it will not differentiate between friend or foe, so be very careful around them. To disarm a tripmine, you can either shoot it or detonate an explosive next to it. It is never advisable to try and bash it off with your crowbar. In earlier versions of Half-Life, you could use these as stairs in deathmatch by placing them on walls and jumping on top of them. However, recent Steam versions have "fixed" this by disabling collision detection on the tripmines.
Snarks
Little aliens that would love to peck your face off. While they are seen in the single-player game as enemies, you can also pick up a pack of your own to throw at the human enemies. They, like the tripmines, don't care about your well-being, so if they run out of stuff to kill, they won't hesitate to start pecking at you. Most devastating when unleashed in groups (i.e. throwing the entire pack at once). After a short while, they will explode into green chunks.