Unlike Haxe, Rust’s major syntactic decisions have been openly discussed and archived. For example, the initial type parameter syntax was [T] (archaea) which then changed to <T> (or, in some places, ::<T> to avoid ambiguity) to make it familiar to C++ programmers.
I see Haxe itself is largely inspired from ActionScript 3, which is in turn inspired by (now-obsolete) ECMAScript 4. This explains why the final forms of both Haxe and Rust look somewhat similar to each other: both are designed to appeal to users of other curly-brace languages (ES vs. C++) and there are some shared challenges requiring the similar syntaxes (macros, for example). Unlike @Manishearth, I don’t think that this is a mere coincidence, but I too agree that this is not really an “influence”.
Although Haxe is cool, I’ve rarely heard in mentioned during Rust’s development. It is not an influence.
Edit: also, the newsqueak / alef / limbo influence was mostly from Graydon’s early preferences, and those languages haven’t had a serious influence on Rust in the entire time I’ve been involved.
While we are at it, Ruby influenced the (now gone) block syntax, but didn’t it also influence the approach of handling basically everything concerning collections with iterators?