well an exploit can make it crash your system or if thier intentions are malicous they can install backdoors own your system make you system
a denial of service bot make it a server what ever it all depends on the
code that is executed once the vulnerability yields control to malicious code

for example you open an exe that is crafted maliciously
in any of the vulnerable app
an exe call Dothis Function ()
looking like this in assembly
0x 401000 call 0x401028
0x401005 test eax,eax

now in stack you will see a pointer to the return value viz return to
401005 from 401000
now if they change the 401005 to 401278 where the malicious code exist
the app will return to 401278 not 401005
and will execute the code that is there in 401278
now what one codes there is upto the wierdest dreams and imagination of the coder

i hope i made it a little clear