The employee will however most often have a few extra things to take care of themselves, compared to being "employed by the books". For example to report local taxes, pension arrangements, health insurance etc. The company isn't usually involved in that, but might pay for it indirectly through a salary that's adjusted for these aspects.
In some countries, local laws require the employee / contractor to have a company (sole proprietor kind). In others, the contracts can be made directly between the business and the individual.
While I have no familiarity, I doubt it is legal in many other countries with a socialist state that requires employers to pay things like national insurance.
Basically if you walk like an employee, and talk like an employee, you're an employee and shouldn't pretend to be an independent contractor and you probably should not set up your own company as you'll be double hit with taxes if they catch you (company taxes for employees and standard employee taxes). That could leave you with several years worth of some serious taxes to back pay.
Don't want to be doom and gloom, but be aware what you're getting yourself into if you're going to pretend to be a consultant/contractor when you're not.
IR35 only applies when there's an intermediary -- usually when you're providing services via a limited company, then taking dividends at the lower tax/NI rate instead of a salary.
If you're self-employed and contracting with a foreign company, then IR35 can't apply (or so I was told when I spoke to HMRC to ask precisely this question).
Now, HMRC could decide that it's not a true self-employment relation. In my case (self-employed, working remotely for a company in the US, limited degree of control by engager, purchasing my own equipment, bearing the risk of invoices not being paid) I think there are enough factors to make it a true self-employment relationship and HMRC's online questionnaire agrees.
Even if you were contracting through a limited company, if you met the self-employment test you'd probably meet the IR35 test when operating through a Ltd. I'd prefer not to risk it -- which is why I went the self-employment route.
I guess that makes senses now thinking about it. I really hate IR35, there's so much grey area.
For more information, and where to find a good lawyer who can firm up such a contract, try http://www.contractoruk.com/ir35/
I'm one of the community managers at SE and I work from my home in Canada where Stack Exchange does not (yet?) have an office. My arrangement is basically that I send in an invoice every month like any contractor would and it is up to me to take care of my own taxes and so on.
From another comment I understand they also have a UK presence. Are you a true-blue employee or a contractor who takes care of their own taxes and affairs, and just issues monthly invoices? If you are an actual employee (in the legal sense), are you employed by the UK or US company, or something else? Do they have to have an address there, or a foreign subsidiary? Presumably there's no German legal entity, so how have they registered there to pay tax?
This is something I'm prospectively interested in doing for my own business, but I'm not sure how I'd make it work from a tax point of view.
The only difference to a standard German employee is this: While in Germany legally the employee owes the wage taxes, they're usually collected by the employer and passed on to the authorities. But the German tax authorities don't like to do that with foreign companies (basically because they can't hunt after them when they don't pay). So from a legal perspective, I pay the wage taxes myself (but the tax office takes care of that as well).
A UK company (or a company of any jurisdiction) can establish a subsidiary in another EU state, in much the same way you could register a NY-incorporated company as a foreign company in CA, but this doesn't appear to be what's happened in this case.
Also if you are an American citizen you have to pay taxes on your worldwide income even if you don't live in the US anymore. There are pretty good exemptions (I think its like the first 90K of income) but you still have to file every year.