//No checking of the input
unsigned int c1,c2,c3,c4;
scanf("%d.%d.%d.%d",&c1,&c2,&c3,&c4);
unsigned long ip = (unsigned long)c4+c3*256+c2*256*256+c1*256*256*256;
printf("The unsigned long integer is %lu\n",ip);
EDIT: For those how are interested on the code produced, GCC is smart enough to replace my multiplication of 256 with shifts left. (In my program I've also called exit):
0x80483d4 <main>: lea 0x4(%esp),%ecx
0x80483d8 <main+4>: and $0xfffffff0,%esp
0x80483db <main+7>: pushl -0x4(%ecx)
0x80483de <main+10>: push %ebp
0x80483df <main+11>: mov %esp,%ebp
0x80483e1 <main+13>: push %ecx
0x80483e2 <main+14>: sub $0x34,%esp
0x80483e5 <main+17>: lea -0x14(%ebp),%eax
0x80483e8 <main+20>: mov %eax,0x10(%esp)
0x80483ec <main+24>: lea -0x10(%ebp),%eax
0x80483ef <main+27>: mov %eax,0xc(%esp)
0x80483f3 <main+31>: lea -0xc(%ebp),%eax
0x80483f6 <main+34>: mov %eax,0x8(%esp)
0x80483fa <main+38>: lea -0x8(%ebp),%eax
0x80483fd <main+41>: mov %eax,0x4(%esp)
0x8048401 <main+45>: movl $0x8048520,(%esp)
0x8048408 <main+52>: call 0x8048320 <scanf@plt>
0x804840d <main+57>: mov -0x8(%ebp),%eax
0x8048410 <main+60>: mov %eax,%edx
0x8048412 <main+62>: shl $0x8,%edx
0x8048415 <main+65>: mov -0xc(%ebp),%eax
0x8048418 <main+68>: lea (%edx,%eax,1),%eax
0x804841b <main+71>: mov %eax,%edx
0x804841d <main+73>: shl $0x8,%edx
0x8048420 <main+76>: mov -0x10(%ebp),%eax
0x8048423 <main+79>: lea (%edx,%eax,1),%eax
0x8048426 <main+82>: mov %eax,%edx
0x8048428 <main+84>: shl $0x8,%edx
0x804842b <main+87>: mov -0x14(%ebp),%eax
0x804842e <main+90>: lea (%edx,%eax,1),%eax
0x8048431 <main+93>: mov %eax,-0x18(%ebp)
0x8048434 <main+96>: mov -0x18(%ebp),%eax
0x8048437 <main+99>: mov %eax,0x4(%esp)
0x804843b <main+103>: movl $0x804852c,(%esp)
0x8048442 <main+110>: call 0x8048330 <printf@plt>
0x8048447 <main+115>: movl $0x0,(%esp)
0x804844e <main+122>: call 0x8048340 <exit@plt>