Back in the early days of video games, everything came on cartridges. To play a game, all you would need to do (in most cases) would be to plug a cartridge into the system, turn it on and go. Sure, there might have been some fiddling around with the connector or blowing into the cartridge here and there, but for the most part things just worked, and you could be playing your game in seconds. As technology marched on and games got more complex, the move to CD-ROM was inevitable, and with it came the necessary evil of loading times. Given the relatively slow read speeds of the various optical disc formats over the years, we've become used to waiting for things to load. And although some games turned out to be worse than others, the sheer amount of data that even the simplest of games requires these days means that there's a good chance you're going to be spending more than your fair share of time waiting for the system to catch up.
But even with as bad as load times could get on the previous generations of systems, it really wasn't until this generation that things really started to get out of hand. Although in the previous console generation the Xbox included a hard drive as standard equipment and the PS2 had one as an optional add-on, it wasn't until the Xbox 360 and PS3 came out that hard drives really became a standardized part of the console landscape. This, combined with Sony's Blu-Ray drive in the PS3 with its large storage capacity but very slow read times, resulted in mandatory installation of games to the hard drive. Perhaps the first game of this generation to be notorious for this was Metal Gear Solid 4, requiring not only an installation when it was played for the first time, but also additional installations at the start of each act (at least until a later patch to the game permitted everything to be installed at once.) Although the installations were relatively short (roughly 8 minutes for the initial installation and another 1-2 minutes each for the smaller installations) it was still a distraction, especially when we might be impatient to just play the freakin' game already.
But when it came to the PS3, that wasn't even the worst of it. Whenever a game on the PS3 is updated with a patch, that update becomes mandatory in order to play the game while online, which means that when the disk was inserted, you are be prompted to either install the update or be signed out of PSN. Some of these patches can be several gigabytes in size, and at times, multiple updates may be required before the game can even be played, and first-party titles were among the worst offenders. When I purchased a copy of LittleBigPlanet Game of the Year Edition to go with my newly purchased PS3 many years ago, it required no fewer than seven patches to be installed before it would even run. I recall Grand Turismo 5 requiring a number of patches out of the box to be playable as well. Combine this with Sony's tendency to make frequent system updates that are mandatory to connect to PSN, and at times you may find yourself needing to download and install several gigabytes of updates just to play a game. This means that in extreme cases you could literally be waiting for hours between the time you insert a disc into the system and the time that the title screen for the game even shows up. Sony has since taken some steps to mitigate this by allowing Playstation Plus users to download patches in the background, and later granting this ability to all users, but this doesn't help much if you buy a new copy of a game. For example, Disgaea 4 (shown above) requires a first-time user to download a 1.7 gigabyte patch before even allowing them to play the game.
Oh, and there's also the problem of storing all those patches. Although it's been years since I've played it and traded it in, Gran Turismo 5 (shown here) still occupies over 7GB of space on my PS3's hard drive with installed data and patches. Given the fact that my PS3 is an older model with only 80GB of space (and some PS3s out there may have as little as 20GB total) this can be a problem if you have more than a few games in your collection.
And yes, the Xbox 360 does behave in much the same way when it comes to patching, but it's far less obnoxious about it than the PS3 is. Patches for Xbox 360 games are rarely more than a few megabytes in size, and can generally be installed in a matter of a few seconds (although, as with all things, there are exceptions.) For better or for worse, patches for Wii games are rare, usually only happening to fix critical bugs that might have made it into production.
With the next generation of consoles approaching rapidly, it seems that patching of games after their release is the new normal when it comes to consoles (and has been the status quo on PCs for years now, although Steam and other similar services generally handle this on their own, with little indication to the user that it's even happening.) Hopefully the PS4 and Xbox One will at least manage to be less obnoxious about it than their predecessors were.