My company was contacted by a firm representing itself as a domain name registration service. They indicated that someone was applying to register domain names across a range of country code domain names such as mycompany.au, mycompany.jp etc. We are registered as mycompany.com. Does this sound legit? What are the downsides for ignoring? Can individuals/companies grab "MyCompany" and apply a range of suffixes to perhaps hit us later with sell offers? Or, if they happen to be in the business we are in - draw traffic to them without us knowing?

It is just scammers trying to frighten you into paying their extortinate fees for something that is no use to you at all.

This issue has been discussed on many webmaster boards months ago. You can simply delete this email and stop worrying, nothing wrong will happen.

They are domainers. They try to earn on it
Do not pay attention unless you are intersted in the such domain names

If your company has registered a trademark, then can try to acquire it. Buying domain in all ext. is only good when you have business in those country.

If you doubt - contact your domain name registrar and ask about that