Perhaps the most commonly seen weapon in the movie, the M1 Garand is used by the majority of the U.S. soldiers seen in the film. The M1 Garand is easily identified by the characteristic ping it makes ejecting its clip after the last round in the en bloc clip is fired. Based on the way everyone can hold these weapons easily, they seem to be light weight models for easy handling in the film, which cuts the realism down a bit.
M1 Carbine
The M1 Carbine appears in the film as the main weapon of Sergeant first class Mike Horvath (Tom Sizemore). It is fitted with a double magazine pouch strapped to the butt stock.
M1A1 Carbine
Members of the 101st Airborne Division as well as other Airborne soldiers use the folding stock variant M1 Carbine, the M1A1.
Springfield 1903A4
The squad's sharpshooter, Private Daniel Jackson (Barry Pepper), carries the sniper version of the Springfield 1903, the 1903A4 bolt-action rifle. The differences include the deletion of the front sight, and the addition of a scope. Jackson is famous for quoting religious scriptures when shooting the rifle, and shooting a German sniper through his own scope similar to a feat accomplished by Gunnery Sergeant Carlos Hathcock in the Vietnam War, although the bullet drop at 400yds would make it impossible to clear all the scope lenses, while Hathcock was far closer to his target, as well as looking down at said target (Hathcock was on a hill, while the enemy sniper was at the base). Jackson clearly has trouble cycling the gun throughout the film due to him being a lefty and the gun being built for right handed shooters. Perhaps he should have found a better method of working the bolt instead of reaching over and shaking the bolt until the extractor ejected the spent shell.
Faulty Scope
During the bell tower sequence, Jackson's Unertl scope is very off from where the bullets hit, likely because he didn't zero it when switching it with his other scope.
It's called wind and leading your shot
Wind cannot do that much at that range, without being gale force winds.
Karabiner 98k
As common with the German soldiers as the M1 Garand is with the Americans, the Karabiner 98k bolt-action rifle is the standard-issue weapon of the German Army. Soldiers during the battle in Ramelle line up armed almost entirely with Kar98k rifles, including Steamboat Willie, who mortally wounds Cpt. Miller with his 98k rifle.
Also note how most of the rifles lack the hooded sights and cleaning rods which usually indicates Russian captures.
Karbiner 98k Sniper
One German sniper is seen armed with a Karabiner 98k sniper rifle fitted with a Zeiss ZF42 scope with a rubber light blocking eye cover (which despite goof reports, is at proper eye relief with him resting his eye on it) and covered in makeshift burlap camouflage who mortally wounds PFC Adrian Caparzo (Vin Diesel) before being killed himself by Private Jackson (Barry Pepper). Jackson shoots the German sniper through his scope, a reference to a shot made by Carlos Norman Hathcock II(a legendary Marine Corps sniper) during the Vietnam War.
Submachine Guns
M1A1 Thompson
The M1A1 Thompson or "fast gun" appears several times in the film, primarily as the main weapon of Captain John H. Miller (Tom Hanks). It is also used by Captain Fred Hamill (Ted Danson) to end a standoff between Miller's men and a group of German soldiers they had stumbled upon. The M1 Thompson was too expensive to produce by the Normandy invasion and the cheaper M1A1, which simply incorporated a fixed firing pin as part of the bolt, made it far easier for mass production as well as cheap too. They were far more commonly issued with 30 round magazines, which is evident on Miller's Thompson.
MP40
Yet another German weapon in the film is the MP40. It's not very often seen, mostly in the scene where Miller's men stumble on a group of German soldiers, and again during the final battle scene in Ramelle.
Some of those look like MP-38's, I think both are used.
Machine Guns and Automatic Rifles
Browning Automatic Rifle M1918A2
As the squad's support gunner, PFC Richard Reiben (Edward Burns) carries a Browning Automatic Rifle M1918A2 or "B.A.R." as his main weapon. The B.A.R. Reiben carries is not his originally issued one, which he claims he lost during the start of the D-Day landing to keep from drowning, and has the bipod removed, making it more into an assault rifle instead of a Light Machine Gun. Further supporting this theory is how he fires it on the faster of the B.A.R.'s two full-auto fire modes, instead of the more efficient slow auto-fire used for support. Reports have said like the M1 Garands in the film, this B.A.R. was lightened for easier use by the actors, making it far easier to shoulder fire the weapon as an assault rifle. (Periods have been added to the B.A.R. abbreviations to make sure no one refers to the weapon incorrectly as a "Bar".)
Browning M1919A4
Among the weapons used by the defenders during the final battle are a pair of Browning M1919A4 or "Browning .30 caliber" machine guns. Both guns eventually run out of ammunition, their users being killed by the Germans. Throughout the scene, the gun in the tower uses a disintegrating belt and Mellish's gun has a fabric belt.
MG42
The German MG42 machine gun makes several appearances in the film; first in bunkers overlooking Omaha Beach during the D-Day landings, then in a machine gun nest at the base of a radar site the squad encounters. The ensuing firefight at the radar site costs them their medic, Cpl. Irwin Wade (Giovanni Ribisi).
Pistols
M1911A1
There are several appearances of the M1911A1 pistol, in the hands of Horvath (Tom Sizemore), Jackson (Barry Pepper), and Miller (Tom Hanks), as well as other members of the squad. Horvath uses it to threaten PFC Richard Reiben (Edward Burns) when he threatens to abandon his squad, later throwing it at a German during the final battle when he runs out of ammo. Miller is seen firing it at an advancing Tiger tank as he lies wounded on the bridge in one of the film's more memorable moments.
Luger P08
During the final assault in Ramelle, a German soldier can be seen using Luger P08 pistol when facing off with Sgt. Horvath and is killed but still manages to wound him with it. The Luger P08 pistol was a very common second line service pistol, with the Walther P38 as the official front line issued sidearm in World War Two. The Luger was still being manufactured during World War Two and was commonly issued to Civilian Polizei as well as Military Police and as request pieces for any military officer at their discretion. There were huge numbers made in World War One and the handgun was in constant manufacture from the time of its initial offering until 1942, when all production switched to the P38. It was common to see Luger 08 Pistols in the hands of vehicle crewmen, crew served weapons, second line units, artillery units. It also ended up in the hands of many front line NCOs as well as officers, since it was still 'regulation' to carry it in the Wehrmacht. Note: there seems to be more photographic evidence of Waffen SS officers wielding the Luger P08 than the Regular army, which may attest to some 'politics' of the ordnance supply chain.
Anti-Tank Weapons
M1A1 Bazooka
The M1A1 Bazooka rocket launcher makes several appearances in Saving Private Ryan. It is first seen in the hands of a U.S. Army soldier under the command of Captain Hamill. Later we see Private James F. Ryan (Matt Damon) use an M1A1 Bazooka to destroy a German half-track. This same Bazooka is later used by Horvath during the final battle to destroy a German Marder self-propelled gun and again in an attempt to destroy a Tiger tank, but unfortunately for our protagonists the rocket is deflected by the tank's heavy armor.
Panzerschreck
During the final battle, one of the German soldiers can be seen carrying a Panzerschreck or "Tank Terror" rocket launcher, but is killed before his weapon can be brought to bear.
Sticky Bomb
While planning the defense of Ramelle, Captain Miller comes up with a unique improvised explosive device he calls a "sticky bomb". It consists of a sock filled with Composition-B explosive with a fuse attached and covered in grease so it sticks where it's placed. Deploying it is a hazardous proposition though; as one soldier is killed when the fuse runs out while he is trying to place it on one of the German tanks, though the bombs do succeed in immobilizing one Tiger tank by destroying its treads. The improvised explosive is apparently inspired by the actual "sticky bomb", the short-lived British No. 74 ST Grenade, which used a purpose-designed super strong resin adhesive instead of axle grease, which was tested and found to be insufficiently sticky.
Molotov Cocktail
During the final battle at Ramelle two soldiers light and throw a pair of Molotov Cocktails off a balcony into a German Marder self-propelled gun below.
Mk-II No. 75 Hawkins Grenade/Mine
Prior to the climactic battle Cpl. Henderson relays to Cpt. Miller that their arsenal of "spitwads" includes Hawkins mines. Later a 101st Airborne soldier is seen placing one on the main street and camouflaging it.
Grenades
Mk 2 Hand Grenade
During the attack on the machine gun nests, the squad uses Mk 2 hand grenades to take out all but one of the Germans manning it, some of which throw the grenades back at them, though thankfully miss. Later, at the final battle in Ramelle, several Mk 2 hand grenades are tossed into a disabled German tank, killing the crew.
M7 Rifle Grenade
During the opening Omaha Beach landing scene we can briefly see a rifle mounted M7 rifle grenade fired from an M1 Garand after the German line has been broken.
Model 24 Stielhandgranate
During the final battle of the film, Private Stanley Mellish (Adam Goldberg) and Corporal Henderson (Maximilian Martini) get several Model 24 Stielhandgranates thrown at them while manning one of the M1919A4 machine guns. Thankfully the two are able to grab and toss the grenades clear before they detonate.
Specialty Weapons
M1 Flamethrower
During the D-Day landing scene Doyle (Glenn Wrage) uses his M1 Flamethrower to clear one of the German bunkers overlooking Omaha Beach, turning the occupants into human torches who are picked off by other soldiers as they emerge, before they are ordered to let them burn. During the opening of the scene, a flamethrower operator gets hit in the pack and gets blown up along with his fellow comrades around him.
M1A1 Bangalore Torpedo
Captain John H. Miller (Tom Hanks) aids some soldiers in employing M1A1 Bangalore Torpedos to clear the barbed wire protecting the German bunkers on Omaha Beach.
Flak 38
A German Flak 38 is crewed by several SS soldiers during the final battle at Ramelle and delivers devastating 20mm flak rounds on Captain Miller's (Tom Hanks) men. It is finally brought down when PFC. Reiben (Edward Burns) flanks it from above and takes out the whole crew single-handedly with his B.A.R.
M2 Mortar
During the final battle in Ramelle, Private Ryan (Matt Damon) and Captain Miller (Tom Hanks) arm 60mm M2 Mortars rounds by banging them against the steel launching base of the mortar tube and throw them like hand grenades at advancing SS soldiers, scoring several kills. While this is possible, they are banging the wrong end, to use the mortar shells in the way they did, they would have to slam the other end against it.