Is there a way to count with macros?

While the ordinary macro system does not enable you to repeat the macro expansion many times, there is no problem with using a for loop in the macro:

macro_rules! many_greetings {
    ($times:expr) => {{
        for _ in 0..$times {
            println!("Hello");
        }
    }};
}

If you really need to repeat the macro, you have to look into procedural macros/compiler plugins (which as of 1.4 are unstable, and a bit harder to write).

Edit: There are probably better ways of implementing this, but I've spent long enough on this for today, so here goes. repeat!, a macro that actually duplicates a block of code a number of times:

main.rs

#![feature(plugin)]
#![plugin(repeat)]

fn main() {
    let mut n = 0;
    repeat!{ 4 {
        println!("hello {}", n);
        n += 1;
    }};
}

lib.rs

#![feature(plugin_registrar, rustc_private)]

extern crate syntax;
extern crate rustc;

use syntax::codemap::Span;
use syntax::ast::TokenTree;
use syntax::ext::base::{ExtCtxt, MacResult, MacEager, DummyResult};
use rustc::plugin::Registry;
use syntax::util::small_vector::SmallVector;
use syntax::ast::Lit_;
use std::error::Error;

fn expand_repeat(cx: &mut ExtCtxt, sp: Span, tts: &[TokenTree]) -> Box<MacResult + 'static> {
    let mut parser = cx.new_parser_from_tts(tts);
    let times = match parser.parse_lit() {
        Ok(lit) => match lit.node {
            Lit_::LitInt(n, _) => n,
            _ => {
                cx.span_err(lit.span, "Expected literal integer");
                return DummyResult::any(sp);
            }
        },
        Err(e) => {
            cx.span_err(sp, e.description());
            return DummyResult::any(sp);
        }
    };
    let res = parser.parse_block();

    match res {
        Ok(block) => {
            let mut stmts = SmallVector::many(block.stmts.clone());
            for _ in 1..times {
                let rep_stmts = SmallVector::many(block.stmts.clone());
                stmts.push_all(rep_stmts);
            }
            MacEager::stmts(stmts)
        }
        Err(e) => {
            cx.span_err(sp, e.description());
            DummyResult::any(sp)
        }
    }
}

#[plugin_registrar]
pub fn plugin_registrar(reg: &mut Registry) {
    reg.register_macro("repeat", expand_repeat);
}

added to Cargo.toml

[lib]
name = "repeat"
plugin = true

Note that if we really don't want to do looping, but expanding at compile-time, we have to do things like requiring literal numbers. After all, we are not able to evaluate variables and function calls that reference other parts of the program at compile time.

As the other answers already said: no, you can't count like this with declarative macros (macro_rules!).

But you can implement the many_greetings! example as a procedural macro. procedural macros were stabilized a while ago, so the definition works on stable. However, we can't yet expand macros into statements on stable -- that's what the #![feature(proc_macro_hygiene)] is for.

This looks like a lot of code, but most code is just error handling, so it's not that complicated!

examples/main.rs

#![feature(proc_macro_hygiene)]

use count_proc_macro::many_greetings;

fn main() {
    many_greetings!(3);
}

Cargo.toml

[package]
name = "count-proc-macro"
version = "0.1.0"
authors = ["me"]
edition = "2018"

[lib]
proc-macro = true

[dependencies]
quote = "0.6"

src/lib.rs

extern crate proc_macro;

use std::iter;
use proc_macro::{Span, TokenStream, TokenTree};
use quote::{quote, quote_spanned};


/// Expands into multiple `println!("Hello");` statements. E.g.
/// `many_greetings!(3);` will expand into three `println`s.
#[proc_macro]
pub fn many_greetings(input: TokenStream) -> TokenStream {
    let tokens = input.into_iter().collect::<Vec<_>>();

    // Make sure at least one token is provided.
    if tokens.is_empty() {
        return err(Span::call_site(), "expected integer, found no input");
    }

    // Make sure we don't have too many tokens.
    if tokens.len() > 1 {
        return err(tokens[1].span(), "unexpected second token");
    }

    // Get the number from our token.
    let count = match &tokens[0] {
        TokenTree::Literal(lit) => {
            // Unfortunately, `Literal` doesn't have nice methods right now, so
            // the easiest way for us to get an integer out of it is to convert
            // it into string and parse it again.
            if let Ok(count) = lit.to_string().parse::<usize>() {
                count
            } else {
                let msg = format!("expected unsigned integer, found `{}`", lit);
                return err(lit.span(), msg);
            }
        }
        other => {
            let msg = format!("expected integer literal, found `{}`", other);
            return err(other.span(), msg);
        }
    };

    // Return multiple `println` statements.
    iter::repeat(quote! { println!("Hello"); })
        .map(TokenStream::from)
        .take(count)
        .collect()
}

/// Report an error with the given `span` and message.
fn err(span: Span, msg: impl Into<String>) -> TokenStream {
    let msg = msg.into();
    quote_spanned!(span.into()=> {
        compile_error!(#msg);
    }).into()
}

Running cargo run --example main prints three "Hello"s.

As far as I know, no. The macro language is based on pattern matching and variable substitution, and only evaluates macros.

Now, you can implement counting with evaluation: it just is boring... see the playpen

macro_rules! many_greetings {
    (3) => {{
        println!("Hello");
        many_greetings!(2);
    }};
    (2) => {{
        println!("Hello");
        many_greetings!(1);
    }};
    (1) => {{
        println!("Hello");
        many_greetings!(0);
    }};
    (0) => ();
}

Based on this, I am pretty sure one could invent a set of macro to "count" and invoke various operations at each step (with the count).