Half-Life

#1 Black Mesa Inbound
The first appearance of the mysterious suited man is on a train parallel to your own shortly before arriving at the Anomalous Materials lab.

#2 Anomalous Materials
Circumnavigate the central computer room on the first level and you'll find a room with two people behind the bullet-proof room where a Scientist later has a face-off with a headcrab. One of these is the Suited Man, and he appears to be having an argument with the scientist there...

#3 Unforeseen Consequences
After your first encounter with the Houndeyes, the suited man appears above you on a walkway heading towards... a zombie and a dead end!

#4 Office Complex
After meeting up with a group of Barneys imploring you to "get topside", the G-Man can be seen straightening his tie behind a red door.

#5 We've got Hostiles
In an L-Shaped corridor with a particularly nasty slippery floor and laser-trigger trap, you come across two scientists pinned down and unable to move. In the far distance beyond them, a suited man stands on a walkway...

#6 Power Up
Look left when entering the turntable chamber where the Gargantua is administering the smackdown to the Marines - the G-Man can be seen as a spectator in the Turntable control room.

#7 Apprehension
When you first enter the "Piston" room (infested with Bullsquids), the suited man can be seen on the far side on a walkway.

#8 Lambda Complex
The G-Man can be seen walking into a portal in a headcrab infested room in the Lambda complex.

#9 Nihlianth
With the Nihlianth slain, Gordon is teleported to an undefined location on Xen where he finally comes face to face with the Man he has been chasing for so long...

Half-Life: Opposing Force

#1 The Manual, "March 3rd"
The first G-Man sighting isn't actually in the game - there are a number of them in the manual! The first goes as follows: "There has been this really weird civie spotted at the base. Rumour has it he's from some government branch looking to recruit; others say he's with some secret research group. I would jump at the chance to join. It would be cool just for the change and the adventure."

#2 The Manual, "March 7th"
"I finally saw the government guy today. I'm not sure he is a g-man, but he was wearing a really uptight suit and carrying a briefcase. He looked more like a lawyer or insurance agent to me. I did notice him checking me out. Several times throughout the day I spotted him just watching me during training. I wonder what he's up to..."

#3 Boot Camp
Nope, still not in the game yet! When running across the courtyard with the soldier doing press-ups on the way to training, look up and to your right - the Suited Man can be seen in a window.

#4 Welcome to Black Mesa
The suited Man can be seen conversing with a Security Guard, through a door just after the Nasty Room of Laser Death(TM)

#5 Welcome to Black Mesa
The Suited Man can be seen operating a Panel to save you from the rising Toxic Sludge. It is impossible to catch him up and show him your gratitude...

#6 "We are pulling out"
Having done you a favour, the Suited Man has you repay it by locking you out of the Helipad. He peers through and walks off. No escape for you then...

#7 Pit Worm's Nest
When dropping into the Star Wars brand waste compactor at the beginning of the chapter, the Suited Man can be seen above, in the control room.

#8 Foxtrot Uniform
When emerging out onto the Dam, look left to see the Suited Man standing on the unreachable Dam control tower.

#9 The Package
After defusing the Black Op's bomb, go inside the Security Guard's hideout. Before descending down the lift to the warehouse, look left through the bullet-proof glass: the Suited Man is bent over the bomb, and there is no way to stop him...

#10 Worlds Collide
The G-Man delivers his final face to face speech with the player aboard an Osprey heading towards... somewhere, or nowhere....

Blue Shift

In the chapter "Insecurity", the G-Man passes you as you wait for a bridge over a body of water, shortly before the disaster

Decay

G-Man appears in an elevator opposite of your own.

Half-Life 2

#1 Point Insertion
The first sighting is obviously the Suited Man's appearance in front of you at the beginning of the game, hinting at what is to come.

#2 Red Letter Day
The monitor in the corner by the HEV suit can be cycled through with the use key ('e'). One of the cameras shows the Suited Man passing through a combine checkpoint completely unharmed and unnoticed...

#3 Route Kanal
When dropping into the box-car with a Man and his Vortiguant pal, look carefully at the Television which the Vortiguant is powering - you can see the Suited Man on it!

#4 Water Hazard
When approaching the first resistance outpost downstream from the shanty town (the Red-Barn), use your Zoom function ('z') and you can see a familiar figure...

#5 Water Hazard
On your way downstream, you come across a Block of Flats in the distance with a large but defective "Breenscreen" on the side. One of the montage of fuzzy images on this screen is the G-Man

#6 Water Hazard
When entering the industrial section downstream from where you get the Airboat upgrade, keep an eye out for the suited man on a walkway above you (this is shortly upstream from the spooky outpost with the windchimes.)

#7 Water Hazard
After taking down the helicopter, get on the hill with the Helipad and use your zoom in the direction of the Dam controls to see the suited Man observing you from afar...

#8 We don't go to Ravenholm
After exiting the mines, follow the traintracks as far as they will go. Find a gap in the train carriages and you'll be able to see the suited man walking beyond, towards a tunnel.

#9 Highway 17
At the first Combine outpost on the coastal road, a soldier can be found looking into a pair of binoculars mounted on the window sill, looking out over the bay. Have a look through them yourself ('e'), and see Resistance leader Cubbage chatting with someone familiar...

#10 Nova Prospekt
On the first of the square monitors you find, one of the camera angles available shows the G-Man walking around completely undisturbed by the Antlion invasion going on around him...

#11 Anti-Citizen One
After Dog completely pwns a squad of combines, an APC and a Dropship, enter the tenement and hear some strange music. Follow the sound and find an unplugged TV transmitting an image of the Suited Man on a boat with a crow on his shoulder. After a few seconds, it turns itself off.

#12 Anti-Citizen One
In the trainstation square, the G-Man can be glimpsed in a similar fashion to sighting #5 - on a malfunctioning screen being pulled down by the resistance fighters.

#13 Dark Energy
Just as the Citadel's core erupts it all stops: time freezes and the G-Man delivers his closing speech.

Ghostly G-Man?

Some speculate that at the end of We don't go to Ravenholm (HL2), a very faint G-Man can be seen as Alyx speaks on a small TV. However, due to the nature of this extremely faint image, on an already disturbed screen, it is impossible to determine whether this is the G-Man or simply Alyx's outline. As a texture based sighting (like #5 and #12), this cannot be verified by finding the "set" from which the image is "broadcast" (which can be found by no-clipping around the map). As such this sighting will not be an official sighting, just a merely "speculative sighting". At least until I see compelling evidence from Valve itself.