Join your queries with a UNION. The way you've got it now, it'll return two results sets.
SELECT [col1], [col2] FROM Contact
UNION ALL
SELECT [col1], [col2] FROM Numar_contact
As DJ KRAZE pointed out in a comment, it might not be a bad idea to wrap this in a sproc or a TVF. But this will work too.
Edit:
I just learned via comments that the two tables are actually unrelated. In light of that, I'd be tempted to use two SqlCommands with two, distinct foreach loops. But if you're sold on this way,
SELECT id_contact, nume_contact, prenume_contact FROM Contact
UNION ALL
SELECT id_contact, numar, NULL FROM Numar_contact
This will align the data from the two tables, but where the second table doesn't have a [prenume_contact] it will select NULL. I might have mixed up the column positions here, since I don't really understand what those names are meant to represent.
Edit 2:
string connString = @"database=Agenda_db; Data Source=Marian-PC\SQLEXPRESS; Persist Security Info=false; Integrated Security=SSPI";
using (SqlConnection conn = new SqlConnection(connString))
{
    try
    {
        conn.Open();
        using (SqlCommand cmd = new SqlCommand("SELECT * FROM Contact", conn))
        using (SqlDataReader rdr = cmd.ExecuteReader())
        {
            while (rdr.Read())
            {
                listBox1.Items.Add(rdr[0].ToString() + " " + rdr[1].ToString() + " " + rdr[2].ToString());
            }
        }
        using (SqlCommand cmd2 = new SqlCommand("SELECT * FROM Numar_contact", conn))
        using (SqlDataReader rdr2 = cmd.ExecuteReader())
        {
            while (rdr2.Read())
            {
                listBox1.Items.Add(rdr2[0].ToString() + " " + rdr2[1].ToString());
            }
        }
    }
    catch { }
}
Edit 3, thanks to insight from Scott Chamberlain:
On the other hand, you might want to perform a JOIN of some kind, most commonly an INNER JOIN. Note that this is an entirely different operation from any we've talked about before.
SELECT Contact.id_contact, Contact.nume_contact, Contact.prenume_contact, Numar_contact.numar
FROM Contact
INNER JOIN Numar_contact on Contact.id_contact = Numar_contact.id_contact
This will tie the two tables together, returning a record for each contact-numar_contact. Again, this is definitely not the same as doing a UNION. Make sure you're aware of the difference before you pick which you want.
Use this if your second table contains data that relates many-to-one to the first table.