Final answer:
Recursive programs can lead to a stack overflow error when there's excessive recursion without proper base cases, causing the program to exhaust memory allocated to the stack.
Step-by-step explanation:
Recursive programs can run out of memory, causing a stack overflow error. When a recursive function is called, its execution context (including parameters, local variables, and return address) is pushed onto the call stack. Recursive functions can be very memory-intensive, especially if the recursion is deep or not properly terminated with a base case. If the stack grows too large due to excessive recursion, the program can run out of space in the stack, leading to a stack overflow error, which is a type of runtime error. It's important for developers to ensure that recursive algorithms have well-defined base cases and to consider the potential risks of stack overflow when designing recursive solutions.