I find the game more appealing knowing there is no safe place to rest, keeping moving staying on your feet and never look back. It's these kinds of emotions that cause you to panic at times and making it hard to think properly and even harder to do actions knowing someone is standing right there ready to kill you.
In most of the games I named you are given choices such as Resident Evil 3 where you can hide, run or be really destructive with your opponent. Such as the beginning in front of Raccoon City Police Station where you are given a choice either to run inside or fight. Choosing to run inside is the safest bet seeing how you just saw one of your comrade die in a painful way from Nemesis's harsh tentacle whip. But to stay and fight would lead to your death unless you are either quite skilled with in the games department or quite skilled in the cheats.
In a lot of other games though such as Clock Tower giving the option to fight is not available to the very end in some cases. Best thing to do is run and hide hoping they wont see you and not to make too much noise so they can hear you (I learned that the hard way in Clock Tower 3.)
Stalkers are an excellent way to keep you on your feet in horror games giving you panic and fear is what horror games are about. Sadly though you don't see much of them anymore hopefully when knew horror games come out on Wii, PS3, and 360 it will be just as frightful as the older games and series.