How do I connect a STOMP client to Wildfly?

It's true WildFly only listens on port 8080 by default (plus port 9990 for management), using HTTP protocol upgrade to switch to different protocols.

However, you can still define additional acceptors for other ports. I don't know whether or not it is possible to use STOMP with protocol upgrade over port 8080, but here's how to configure an additional Netty acceptor for port 5445:

<extension module="org.jboss.as.messaging"/>

<subsystem xmlns="urn:jboss:domain:messaging:2.0">
    <hornetq-server>
        <journal-file-size>102400</journal-file-size>
        <connectors>
            <http-connector name="http-connector" socket-binding="http">
                <param key="http-upgrade-endpoint" value="http-acceptor"/>
            </http-connector>
            <http-connector name="http-connector-throughput" socket-binding="http">
                <param key="http-upgrade-endpoint" value="http-acceptor-throughput"/>
                <param key="batch-delay" value="50"/>
            </http-connector>
            <in-vm-connector name="in-vm" server-id="0"/>
        </connectors>
        <acceptors>
            <http-acceptor name="http-acceptor" http-listener="default"/>
            <http-acceptor name="http-acceptor-throughput" http-listener="default">
                <param key="batch-delay" value="50"/>
                <param key="direct-deliver" value="false"/>
            </http-acceptor>
            <netty-acceptor name="stomp-acceptor" socket-binding="messaging-stomp">
                <param key="protocols" value="STOMP"/>
                <param key="connection-ttl" value="30000"/>
            </netty-acceptor>
            <in-vm-acceptor name="in-vm" server-id="0"/>
        </acceptors>
        <security-settings>
            <security-setting match="#">
                <permission type="send" roles="guest"/>
                <permission type="consume" roles="guest"/>
                <permission type="createNonDurableQueue" roles="guest"/>
                <permission type="deleteNonDurableQueue" roles="guest"/>
            </security-setting>
        </security-settings>
        <address-settings>
            <!--default for catch all-->
            <address-setting match="#">
                <dead-letter-address>jms.queue.DLQ</dead-letter-address>
                <expiry-address>jms.queue.ExpiryQueue</expiry-address>
                <max-size-bytes>10485760</max-size-bytes>
                <page-size-bytes>2097152</page-size-bytes>
                <message-counter-history-day-limit>10</message-counter-history-day-limit>
            </address-setting>
        </address-settings>
        <jms-connection-factories>
            <connection-factory name="InVmConnectionFactory">
                <connectors>
                    <connector-ref connector-name="in-vm"/>
                </connectors>
                <entries>
                    <entry name="java:/ConnectionFactory"/>
                </entries>
            </connection-factory>
            <connection-factory name="RemoteConnectionFactory">
                <connectors>
                    <connector-ref connector-name="http-connector"/>
                </connectors>
                <entries>
                    <entry name="java:jboss/exported/jms/RemoteConnectionFactory"/>
                </entries>
            </connection-factory>
            <pooled-connection-factory name="hornetq-ra">
                <transaction mode="xa"/>
                <connectors>
                    <connector-ref connector-name="in-vm"/>
                </connectors>
                <entries>
                    <entry name="java:/JmsXA"/>
                    <entry name="java:jboss/DefaultJMSConnectionFactory"/>
                </entries>
            </pooled-connection-factory>
        </jms-connection-factories>
        <jms-destinations>
            <jms-queue name="ExpiryQueue">
                <entry name="java:/jms/queue/ExpiryQueue"/>
            </jms-queue>
            <jms-queue name="DLQ">
                <entry name="java:/jms/queue/DLQ"/>
            </jms-queue>
        </jms-destinations>
    </hornetq-server>
</subsystem>

<socket-binding-group name="standard-sockets" default-interface="public" port-offset="${jboss.socket.binding.port-offset:0}">
    <socket-binding name="messaging-stomp" port="5445"/>
</socket-binding-group>

In addition, you'll have to create a user account with role guest via add-user.sh. This account will be used by the STOMP client.

Tested on WildFly 8.2.0.Final.