The answer is No and Yes. Theoretically,
there is no limit. However, the kernel may be
configured to allow only a limited amount
of memory per process and/or user. You can find
out what the system resource limits are on your
particular UNIX system using the system
call "getrlimit()" (man section 2). The following
C program can be compiled and run as any ordinary
user...

================== SNIP ========================
/*
* Filename - getlimits.c
*
* Description - display system resource limits and
* test allocating large blocks of memory.
*
*/

#include <sys/time.h>
#include <sys/resource.h>
#include <unistd.h>
#include <stdio.h>
#include <stdlib.h>

main(int argc, char **argv)
{
struct rlimit rlim;
void *p;

getrlimit(RLIMIT_CPU, &rlim);
printf("CPU: cur - %ld max - %ld\n", rlim.rlim_cur, rlim.rlim_max);
getrlimit(RLIMIT_FSIZE, &rlim);
printf("FSIZE: cur - %ld max - %ld\n", rlim.rlim_cur, rlim.rlim_max);
getrlimit(RLIMIT_DATA, &rlim);
printf("DATA: cur - %ld max - %ld\n", rlim.rlim_cur, rlim.rlim_max);
getrlimit(RLIMIT_STACK, &rlim);
printf("STACK: cur - %ld max - %ld\n", rlim.rlim_cur, rlim.rlim_max);
getrlimit(RLIMIT_CORE, &rlim);
printf("CORE: cur - %ld max - %ld\n", rlim.rlim_cur, rlim.rlim_max);
#ifdef LINUX
getrlimit(RLIMIT_RSS, &rlim);
printf("RSS: cur - %ld max - %ld\n", rlim.rlim_cur, rlim.rlim_max);
getrlimit(RLIMIT_NPROC, &rlim);
printf("NPROC: cur - %ld max - %ld\n", rlim.rlim_cur, rlim.rlim_max);
#else
getrlimit(RLIMIT_VMEM, &rlim);
printf("VMEM: cur - %ld max - %ld\n", rlim.rlim_cur, rlim.rlim_max);
getrlimit(RLIMIT_AS, &rlim);
printf("AS: cur - %ld max - %ld\n", rlim.rlim_cur, rlim.rlim_max);
#endif
getrlimit(RLIMIT_NOFILE, &rlim);
printf("NOFILE: cur - %ld max - %ld\n", rlim.rlim_cur, rlim.rlim_max);
#ifdef LINUX
getrlimit(RLIMIT_MEMLOCK, &rlim);
printf("MEMLOCK: cur - %ld max - %ld\n", rlim.rlim_cur, rlim.rlim_max);
#endif

if((p = malloc(100000000)) == NULL)
{
printf("malloc 100M failed\n");
}
else
{
printf("malloc 100M succeeded\n");
}
if(p) free(p);
if((p = malloc(500000000)) == NULL)
{
printf("malloc 500M failed\n");
}
else
{
printf("malloc 500M succeeded\n");
}
if(p) free(p);
return 0;
}

================== SNIP ========================

The output (on Linux) should look somthing like...

$ getlimits
CPU: cur - 2147483647 max - 2147483647
FSIZE: cur - 2147483647 max - 2147483647
DATA: cur - 2147483647 max - 2147483647
STACK: cur - 8388608 max - 2147483647
CORE: cur - 1024000000 max - 2147483647
RSS: cur - 2147483647 max - 2147483647
NPROC: cur - 2048 max - 2048
NOFILE: cur - 1024 max - 1024
MEMLOCK: cur - 2147483647 max - 2147483647
malloc 100M succeeded
malloc 500M succeeded