An infinite combo is a combo that lasts for as long as the player executing it enters the right commands. Infinite combos usually require specific commands and tight timing to keep them going.
Good or Bad?
Opinions on infinites differ depending on the game and the person, though it's a widely accepted and encouraged tactic in Marvel vs. Capcom 2. While this may seem incredibly absurd to some, it isn't so ridiculous when considering there are three characters on each team. This means an infinite performed to completion isn't really a 100% combo, but a technical 33.3% combo, keeping in mind the victim still has two other characters. For MvC2 in particular, infinites were very difficult to execute so most players would stop the combo at a point and go for a reset rather than risk dropping the combo and losing their advantage in pursuit of killing the opponent's point character.
In recent years, fighting game developers have made a point to keep infinites out of their games. For instance, when Super Street Fighter 4 was first released, Fei Long could perform an infinite in which he uses hard punch, followed by hard chicken wing, followed by another hard punch, followed by another hard chicken wing, etc. This infinite could only be performed against Juri. Soon after, Capcom released a patch that made this infinite no longer possible. Capcom has released several patches for Marvel vs. Capcom 3 that have removed infinites, despite the series' history. It should be noted that several characters can perform Infinite combos while in X-Factor of various levels, which boosts speed and damage. These infinites have not been removed by the previously mentioned patches.
Since the release of Ultimate Marvel vs. Capcom 3, a few infinites have been discovered. The one using Wolverine's berserker rage move in tandem with Spencer's slant shot assist. This was the only infinite to be patched out. One infinite involved a glitch with Viewtiful Joe's shocking pink assist, such that if the bomb is blocked by the point character, the assist can be called again. The infinite itself used Spencer and his up-grapple move to grab the opponent and put him into a hard knockdown state, calling the shocking pink assist, and blocking it so that Spencer can up-grapple the OTG'ed opponent again, and call the shocking pink assist again, etc. A more recent infinite involves TACing into trish where she juggles the opponent in the air indefinitely because TACs cap the hit stun decay. This characteristic of Team Aerial Exchanges also allowed for a chun li infinite.
Skullgirls and its IPS
Before it's release, Skullgirls Programer/Designer "Mike Z" touted his game's "Infinite Protection System" though provided little insight into the inter workings of the system commenting in an interview: "I don't want to talk about how it actually works, because I don't want it to get stolen before we actually put the game out". Around the time of the game's release, he shared how the system works. Infinites do exist in the game, but they can be broken out of by the opponent once the IPS system kicks in (indicated by a change in the color of the hit sparks). Combos have 5 stages, as a combo progresses, the level of the combo increases. Once a character combos the opponent with a chain starting with the same normal twice, the system kicks in. Many long combos involve the same chain being executed several times but starting with a different normal.