Perform a clean Apache install:

sudo apt-get install apache2

After that copy original configuration files:

cp /etc/apache2/apach2.conf /etc/apache2/apache2.conf.org
cp /etc/apache2/sites-available/default /etc/apache2/sites-available/default.org
cp /etc/apache2/sites-available/default-ssl /etc/apache2/sites-available/default-ssl.org

To prevent users from getting a directory listing add the next line to the bottom of your apache2.conf:
Options -Indexes

A fresh apache install has the following modules installed

apachectl -t -D DUMP_MODULES

Loaded Modules:
core_module (static)
log_config_module (static)
logio_module (static)
version_module (static)
mpm_prefork_module (static)
http_module (static)
so_module (static)
alias_module (shared)
auth_basic_module (shared)
authn_file_module (shared)
authz_default_module (shared)
authz_groupfile_module (shared)
authz_host_module (shared)
authz_user_module (shared)
autoindex_module (shared)
cgi_module (shared)
deflate_module (shared)
dir_module (shared)
env_module (shared)
mime_module (shared)
negotiation_module (shared)
php5_module (shared)
reqtimeout_module (shared)
setenvif_module (shared)
status_module (shared)
Syntax OK

As you can see the rewrite module is missing from this list. You can simple active this module by executing:

a2enmod rewrite