First prime number larger than given integer
Things you could improve

Efficiency


As @rolfl stated, you want to use a Sieve of Eratosthenes (+1 to that answer).


I can't see if you are doing this already, but you should be compiling with your compiler's highest optimization level.  With GCC for example, this would be -O3.


Portability


Keep in mind to adhere to the standards as closely as possible, because a system that supports C must adhere to the standards as well. 
If you want your program to be as portable as possible, take a look into the AutoTools suite for packaging your program.  This is a bit extreme in your case, since you aren't using external libraries, and your program doesn't have a lot of system dependencies.


Standards


You don't have to return 0 at the end of main(), just like you wouldn't bother putting return; at the end of a void-returning function. The C standard  knows how frequently this is used, and lets you not bother.


  C99 &amp; C11 §5.1.2.2(3)
  
  ...reaching the } that terminates the main() function returns a
  value of 0.

Use the standard library &lt;stdbool.h&gt; instead of defining your own boolean values.


#define PRIME_FALSE   0     /* Constant to help readability. */
#define PRIME_TRUE    1     /* Constant to help readability. */



It still helps with readability.  And since it is part of the standard in C, systems are guaranteed to have it if they support C.


Syntax/Styling


Don't use goto.  



Yes, there are some rare situations where you may find it necessary to use it.  This is not one of them.  A simple break; will suffice in it's place, since you are only breaking out of the inner loop.
Right now you are using a somewhat odd way to test if you have an integer input into the command line arguments.


if (sscanf(argv[1], "%i", &amp;intvar) != 1)



Use argc to test the number of arguments input into the program instead, and isdigit to test if the input contains numbers.

if (argc != 2 || !isdigit(**(argv+1))) printf("Please use an integer parameter to compute the next prime.\n");


Then convert that input into an integer.

int intvar = atoi(*(argv+1));


Note that the order I put it in is important.  We want to test argc first, so we put it first in the test conditional.  If that fails, the second part on the other side of the || isn't even evaluated, and the statements following the conditional are executed.  If we switched those tests around, undefined behavior could occur if we didn't enter in a command line argument.
Use puts() instead of printf() when you aren't formatting your strings.  This allows you to not worry about the newline (\n) character at the end of your printed out strings.

puts("Please use an integer parameter to compute the next prime.");

You don't modify the value of intval within your nextprime() function, therefore the parameter should be declared constant.

int nextprime(const int inval)

You can reduce down one of your test conditionals.


if (inval == 1)
    return (2); /* Easy special case. */
if (inval == 2)
    return (3); /* Easy special case. */



if (inval == 1 || inval == 2) return (inval + 1); /* Easy special case. */