Assuming someone is doing some big computations (I know that's relative... and I'm not gonna specify the nature of the operation just to keep the question open, it may be sorting data, searching for elements, calculating the prime factors of a really long number... ) using badly designed, brute force algorithmes or just an itterative process to get the results, can this approach have any bad effetcs on the cpu or the ram over a long period of time ?
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Intensive processing will increase the heat generated by the CPU (or GPU) and even the RAM (to a much smaller degree).
Recent CPU chips have the ability to slow themselves down once the heat exceeds certain thresholds to prevent damage to the CPU. That would typically indicate a failure in the cooling system though.
I do not believe there are much other issues other than electricity consumption and overheating risks.