Once you play enough games, you actually tend to ignore requirements, but as RazerZ explained and as bystander said, there's a reason they're called requirements.
Generally, you use minimum requirements as a guide for how the game will run, as recommended ones mostly are random pieces of hardware where tests have been made...
Depending on how far below or above you're from them, you configure and play the game accordingly. Sure, if you want to play a high specs game at high settings, you're going to need a high-end rig (which doesn't necessarily mean >1200$), but that doesn't forbid you from lowering the game's settings or, if the hardware can hold it up, overclocking the system.
Still, it's a matter of fact that, if a game requires a minimum of 4gb RAM and you own 2, or if it requires a minimum of a 2 year old discrete GPU and yours is an embedded, you're not going to play the game easily (or, worst case scenario, at all).
If this still isn't clear for you, or you feel we misunderstood you again, why don't you give us some examples? Start by listing your system specs and the games you are playing or want to play on it; you may also link us a video of what you mean.