Is language {M | M halts and print "Hello World"} recursively enumerable?
Enumerate all turning machines $M_1, M_2, \dots, $ and simulate them in a dovetail fashion, i.e., proceed in rounds: 


In the first round simulate $M_1$ for $1$ step;
In the second round simulate $M_1$ and $M_2$ for one (more) step each;
In the third round simulate  $M_1$, $M_2$ and $M_3$ for one (more) step each;
...


In general, at the $i$-th round you perform one additional step for all turning machines in $\{ M_1, \dots, M_i \}$ that have not yet halted. Whenever a Turing machine $M$ halts, check if its output is "Hello World" and, if so, return $M$.