The ID field will definitely work. If you wanted a larger number you could just add 10,000 to it and it will still be unique.
Other ways of doing this get more involved. You can store a value in the wp_options table, and then fetch, increment, save, but you have a small window of opportunity where two people could end up with the same number, so you need to check for that and repeat if there was a collision. You can generate MD5 (or SHA1) hashes from some chosen bits of user info, but this will give you a big, nasty string of characters. This can be useful when generating a UUID (Universally Unique ID) across multiple systems because the chance of collision is vanishingly small.