Rendering Pipeline Lag (PCs/Consoles take time to process information in the frame buffer and send it to a display device) - This is also dependent on Frame Rate, at 60FPS for instance the minimum theoretical Input Lag is ~17ms, if it drops down to 30FPS the minimum is 32ms, at 120FPS this delay is theoretically smaller
Input Lag - Mouse/Controller - this is usually negligible at somewhere around ~10ms, sometimes less, sometimes more. On Macs for instance there was an issue that caused 32ms of Mouse Lag: http://d43.me/blog/1205/the-cause-for-all-your-mac-os-x-mouse-annoyances/
Then there's just engines not being optimized or devs not caring much about latency that add on top of that.
There is an interesting article about The initial Hardware Lag for consoles here on Digital Foundry: http://www.eurogamer.net/articles/digitalfoundry-lag-factor-article and it can vary from 70-200ms alone (which comes rather close to your reaction time, and this is before we apply the next two factors)
Here's a final list of all the games I tested for this feature. Not all made it into the videos, so this handy table represents all of my findings. Probably the biggest surprise after GTA was the amount of lag built into LEGO Batman - 133ms on a 60FPS game. What is important to note is that these findings are very context-sensitive. Yes, COD4 appears to be more responsive than World at War, but in different selections of levels per game you could easily reverse that. In this respect, these results do have an element of randomness about them, though it is no secret that for the most scenarios, COD4 does outperform its pseudo-sequel.
Game - Latency Measurement
Burnout Paradise - 67ms
BioShock (frame-locked) - 133ms
BioShock (unlocked) - as low as 67ms
Call of Duty 4: Modern Warfare - 67ms-84ms
Call of Duty: World at War - 67ms-100ms
Call of Juarez: Bound in Blood - 100ms
Forza Motorsport 2 - 67ms
Geometry Wars 2 - 67ms
Guitar Hero: Aerosmith - 67ms
Grand Theft Auto IV - 133ms-200ms
Halo 3 - 100ms-150ms
Left 4 Dead - 100ms-133ms
LEGO Batman - 133ms
Mirror's Edge - 133ms
Street Fighter IV - 67ms
Soul Calibur IV - 67ms-84ms
Unreal Tournament 3 - 100ms-133ms
X-Men Origins: Wolverine - 133ms
In-game latency, or the level of response in our controls, is one of the most crucial elements in game-making, not just in the here and now, but for the future too. It's fair to say that players today have become conditioned to what the truly hardcore PC gamers would consider to be almost unacceptably high levels of latency to the point where cloud gaming services such as OnLive and Gaikai rely heavily upon it.
The average videogame runs at 30FPS, and appears to have an average lag in the region of 133ms. On top of that is additional delay from the display itself, bringing the overall latency to around 166ms. Assuming that the most ultra-PC gaming set-up has a latency less than one third of that, this is good news for cloud gaming in that there's a good 80ms or so window for game video to be transmitted from client to server.
But in the meantime, while overall "pings" between console and gamer remain rather high, the bottom line seems to be that players are now used to it, to the point where developers - like Infinity Ward - centred on getting the very lowest possible latencies are using that to give their games an edge over the competition. Call of Duty's ultra-crisp response is one of the key reasons why it's a cut above its rivals, and it's a core part of a gameplay package that will once again top the charts this Christmas.
Display Lag - CRTs didn't really have any, LCDs often using things like Noise Reduction, any sort of Image Processing, Scaling or Correction can add a lot of Lag, which can be anywhere around 20-30ms or more depending on configuration, there's also the initial pixel response times that manufacturers usually report to be added.
Online Gaming - Network Lag/Connection Delay let's say 40-50ms in some of the best cases
You can't simply look at this from an "academic" standpoint saying that there is 0ms Hardware Lag between what is being displayed and the user and further more that there are no psychological and cognitive effects in play from something going smoother and not appearing to be stalling because that's simply not the reality, and any part of the chain that decreases Lag is preferable in the first place, having higher FPS can cut down latency in the rendering pipeline (e.g. for 60FPS to ~17ms from over 32 for 30FPS) and having 120FPS can cut it down further to around ~8ms, which won't really be noticeable anymore under any circumstances.
And again... I've done this stuff, I have played games using a CRT monitor (with literally no lag) a lot in the past, and believe me there's a damn clear/noticeable difference there in moving your mouse around/aiming or trying to make that jump with an extremely smooth 120FPS over even 60FPS.
Please stop spreading misinformation and read up on the issue or grab yourself a CRT, install Quake 3 or similar and try it yourself, it's always the best experience xD
As More Fun To Compute said, any significant decrease in latency in that chain will give whoever a perceivable advantage over another player (because he will be the first to shoot/click/attack/whatever), this isn't true for all kinds of games but those based on reaction times as people have said fast-paced First Person Shooters and Fighting games especially or all these games where you're supposed to press buttons quick on a controller.