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Don't replace the cassette and chain at the same time if one of them is still in decent shape. Usually they wear unevenly - the chain might already be stretched while the cassette is fine, or vice versa. If you put a new cassette on an old chain, they won't work well together and the new cassette will wear out fast. The same thing happens if the chain is new but the cassette is worn out. So first you need to figure out what exactly needs replacing.
Check the chain for stretch - there are special gauges for this, but you can eyeball it too. If it sags or is loose, it's time to change it. Look at the cassette visually: if the teeth look like shark teeth, pointy and jagged, then it's worn out. If both parts look relatively okay, you can get away with just one replacement.
If your bike has lived an intense life and both parts are clearly worn, then yeah, it makes sense to update both. But if the bike just sat around or was ridden gently, one replacement is probably enough. The main thing is not to put something new on something completely trashed.
It depends on how "old" the bike is and how often you ride it. If the bike's still in use and the chain and cassette are genuinely worn out - go ahead and change them, otherwise you'll get skipping when you shift and lose the pleasure of riding. But the previous answer's right about uneven wear: before you replace both parts, check each one separately. Sometimes just a new chain is enough and the cassette will last longer, or it could be the other way around - that'll save you some money.
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