The GraphQL wire adapter can be used to fetch/retrieve and display Custom Metadata Type records in Salesforce Lightning Web Component without Apex.

Sample Custom Metadata Type:

Sample Lighting Web Component:

HTML:

<template>
    <lightning-card>
        <div class="slds-m-around_medium">
            <div style="width: 250px;">
                <lightning-combobox
                    name="Sample"
                    label="Sample"
                    value={value}
                    placeholder="Select Sample"
                    options={options}
                    onchange={handleChange}>
                </lightning-combobox>
                <br/>
            </div>
            <template if:true={value}>
                <p>Selected Value: {value}</p>
            </template>
        </div>
    </lightning-card>
</template>

JavaScript:

import { LightningElement, wire } from 'lwc';
import { gql, graphql } from 'lightning/uiGraphQLApi';

export default class SampleLightningWebComponent extends LightningElement {

    value;

    @wire( graphql, {
        query: gql`
            query getSamples {
                uiapi {
                    query {
                        Sample__mdt {
                            edges {
                                node {
                                    Label__c : Label__c {
                                        value
                                    }
                                    Value__c : Value__c {
                                        value
                                    }
                                }
                            }
                        }
                    }
                }
            }
        `
    })
    graphql;

    get options() {

        console.log( this.graphql );
        return this.graphql.data?.uiapi.query.Sample__mdt.edges.map(
            ( edge ) => ( {
                label: edge.node.Label__c.value,
                value: edge.node.Value__c.value
            }
        ) );
    }

    handleChange( event ) {
        this.value = event.target.value;
    }

}

js-meta.xml:

<?xml version="1.0" encoding="UTF-8"?>
<LightningComponentBundle xmlns="http://soap.sforce.com/2006/04/metadata">
    <apiVersion>63.0</apiVersion>
    <isExposed>true</isExposed>
    <targets>
        <target>lightning__Tab</target>
    </targets>
</LightningComponentBundle>

Output: