The English equivalents are multiple and confusing.
1. enclosure: something enclosed in a letter, usually. It implies an envelope, in which you can enclose something.
At the end of a business letter, after your signature, you can write Enclosure(s)
2. exhibit: the Anlage to a document filed at court. And also, I gather, often in contracts in the USA, and at least also in statutory declarations in England.
There is an objection to this in a recent comment from a German lawyer, who says that only the document itself and not the Anlagen is evidence (ein Beweisstück) in German law.
I counter this by saying that there are two meanings of exhibit, in which Merriam-Webster's Dictionary of Law agrees with me: a) evidence b) a document labeled with an identifying mark (as a number or letter) and appended to a writing (as a brief) to which it is relevant. Gifis and OED don't agree, but Black's does:
exhibit 1. a document, record, or other tangible object formally introduced as evidence in court.
2. A document attached to and made part of a pleading, motion, contract, or other instrument.
I've actually been checking a discussion on the legaltranslators list at Yahoo Groups, and a translator in the USA had a huge file of US contracts collected over the years - and every one used the term exhibit. This was new to me, but see quote from Black's above.
At all events, in my experience a pleading (Schriftsatz) is not evidence in English law, and a contract certainly is not evidence at the date it is signed, so the question doesn't arise.
3. attachment: this refers to anything you attach to email, including a document, an image, an MP3 file or any other file. It should only be used in email, but I imagine its use is growing.
There are a couple of narrow usages that are also fairly clear:
4. In Austria, samt Anhang (s. A.), referring to a sum of money, means something like with supplementary charges
5. In financial statements, Anhang can be translated Notes to financial statements.
After this, we get into the murky waters of differences between British and American English and what to do with contracts and statutes.
Some available terms are schedule, annex(e), appendix, rider, supplement. (Apparently South Africa and some other places use annexure).
6. appendix is a great neutral term for those working for both Britain and the USA. It's widely understood, perhaps from its use in books, and is acceptable in both countries. I'm not the only translator who uses this as 'neutral'. I encountered one other who uses appendix all the time, except for very technical appendixes (appendices, if you like) to contracts, which he calls technical specifications.
Unlike appendix, annex(e) and schedule are terms most often used in legalese, and therefore tempting to use. I only say the minimum about these two important terms below, but may expand later.
7. schedule - it seems more British to me than annexe. It is commonly used in statutes as well as contracts.
8. annex(e), without the e seems more common to me in US English. Garner's Dictionary of Modern Legal Usage disagrees, saying it appears more frequently in BrE than AmE, and in both more frequently in legal than nonlegal writing. But Garner doesn't mention schedule at all, at least not under S.
My experience is that what I write often goes to people without English mother tongue all over Europe or the world. Sometimes it goes specifically to the USA, but then usually to lawyers. But for many translators I am in contact with, they are in the UK and what they translate into English is more 'localized'. A topic for another entry.
I've never seen Appendix used for an original English Contract Schedule. But there's always a first time - like the translation of 'Codicil' to a Deed!
In accounting, I would say that a "schedule of accounts" is something like a "Positionsübersicht".
I would wager that 'attachment' became the standard term in connection with the email because it was already the standard US term for any document(s) physically attached to the document in question. For this you can credit the stapler. 'Enclosure(s)' became reserved for papers that were NOT stapled to the cover letter. (Our tax forms instruct us to 'attach' some items to the return and 'enclose, but do not attach' the cheque sent in payment.)
I just had a note from my health insurance company, telling me not to use paperclips but to put everything loose in the envelope. It tells me, rather condescendingly, that more than 200 tonnes of steel could be saved in Germany per year if each of the 17 million Germans who work in an office saved one paperclip a day. If I stop using paperclips (or staples, presumably), I have a chance of winning a book called 'Einfach die Welt verändern im Job' (How to change the world in your job). I hope I don't win the book - I'd prefer to save those particular trees.
When such a notarial instrument needs to be taken apart e.g. because of a mis-translation(s), it is called 'dis-annexing' or 'dis-annexure', whether or not these ancient annexure terms are in the Oxford Eng., Miriam Webster or any Anglo-Eng. law dictionaries.