Multi-dimensional arrays are beneficial in scenarios where data is naturally structured in more than one dimension and this structure needs to be preserved for clarity or computational efficiency. A common example is in matrix operations, such as those found in mathematical computations, graphics processing, and scientific simulations, where a two-dimensional array can represent a matrix. Another scenario is in game development, where a two-dimensional array could represent a game board, like a chessboard, and a three-dimensional array could represent a 3D space for games with three-dimensional graphics. Multi-dimensional arrays are also useful in applications that require representing and processing data in tabular form, such as spreadsheets or database records. In these cases, using multi-dimensional arrays can make the code more readable and aligns more intuitively with the real-world representation of the data, besides potentially offering more efficient data processing.

Contiguous memory allocation is crucial for arrays as it enables quick and efficient access to their elements. When array elements are stored in contiguous memory locations, it allows for direct indexing, where the memory address of any element can be calculated and accessed in constant time using the base address of the array and the element's index. This direct access is much faster than if elements were scattered throughout memory, which would require additional steps to locate each element. Contiguous allocation also optimises the use of the CPU cache. Since arrays store elements next to each other, when one element is brought into the cache, its neighbouring elements are also likely to be cached, reducing the need for frequent memory access and thereby increasing performance. However, the downside of contiguous memory allocation is that it requires a single, unbroken block of memory, which can be a limitation when dealing with very large arrays or in systems with fragmented memory.

The choice of programming language significantly influences how arrays are used and their functionalities. Different languages have different syntaxes, capabilities, and limitations regarding array operations. For instance, in languages like C and C++, arrays have a fixed size and do not offer built-in methods for resizing, whereas languages like Python and Java provide dynamic arrays (lists in Python and ArrayList in Java) that can resize automatically. The indexing of arrays also varies; most languages use zero-based indexing, but some, like MATLAB, use one-based indexing. Moreover, the type of elements an array can store varies: languages like Java are strict about data types, while languages like Python can store multiple data types in the same array. Some languages offer advanced features such as multi-dimensional arrays or special functions for array manipulation, which can significantly affect how arrays are implemented and used in different programming environments.

Accessing an array element outside of its bounds, commonly known as an "array index out of bounds" error, can have several consequences, ranging from incorrect program behaviour to program crashes. This happens because accessing an out-of-bounds index means the program is trying to read or write to a memory location not allocated for the array, which could be storing other data or be entirely inaccessible, leading to undefined behaviour. To prevent this, programmers must ensure that the indices used to access array elements are always within the valid range. This can be done by implementing checks before accessing elements, such as comparing the index against the array's length (in languages where this information is readily available) or using conditional statements to ensure the index is greater than or equal to zero and less than the array's upper bound. Some programming languages offer built-in functions or exceptions to handle such cases, alerting the programmer during runtime or even compile-time about potential out-of-bounds access.

In languages like C, the size of a static array cannot be modified once it is declared, as the size is fixed at compile time. However, in Java, while the size of a traditional array cannot be changed after its creation, the language offers dynamic array-like data structures, such as ArrayList, which can be resized. If resizing is required in C, one common approach is to create a new larger array and copy the elements from the old array to the new one. This process, however, is not very efficient as it involves memory allocation and element-by-element copying. A more efficient approach in C is to use dynamic memory allocation with pointers and the malloc and realloc functions, which allow for dynamic resizing of an array at runtime, though this adds complexity in terms of memory management. In Java, the use of ArrayLists simplifies this process significantly, as they automatically resize themselves when elements are added or removed, abstracting away the details of array resizing from the programmer.