If I'm opening a hosting company and would there be any legal reason or requirement to obtain the home or business addresses of my clients?
In general, you are under no obligation to keep address records - at least, I wasn't able to find any laws that impose a general obligation on businesses.
However, there may be laws that impose such requirements on certain types of businesses - for example, financial institutions are required to verify the identity of their customers, and address records are almost certainly part of the process for doing so.
Similarly, if you are professionally insured (for instance, in the legal sector), you may be contractually required to complete an identity check, which maintaining address records may form part of. Of course, being a hosting company, this might not apply to you, though if you have insurance, you should probably check the terms, or ask them for information on this matter.
Lastly, although you may have dismissed this as a legal reason to do so, you may wish to maintain address records in order to, if the need arises, verify the identity of a customer who might bring a claim against you, or to dispute the identity of a party attempting to do so - the less information you have, the harder it would be for you to verify that they are, in fact, a customer, and this could result in unwarranted judgements against you.
Of course, because you're trading internationally, it's a bit difficult to ensure that no laws, anywhere, require this of you - some countries have laws with extraterritorial effect.