How to Increase the Number of Crosssell Items in Cart?

You're going to need to implement your own module to do so

app/code/local/MyCompany/Checkout/Block/Cart in Crosssell.php

 class MyCompany_Checkout_Block_Cart_Crosssell extends Mage_Catalog_Block_Product_Abstract
{

//     /**
//      * Items quantity will be capped to this value
//      *
//      * @var int
//      */
//     protected $_maxItemCount = 100;

//     /**
//      * Get crosssell items
//      *
//      * @return array
//      */

public function getItemCount()
{
         return count($this->getItems());
}

public function getItems()
{
    $items = $this->getData(\'items\');
    if (is_null($items)) {
        $items = array();
        $ninProductIds = $this->_getCartProductIds();
        if ($ninProductIds) {
            $lastAdded = (int) $this->_getLastAddedProductId();
            if ($lastAdded) {
                $collection = $this->_getCollection()
                    ->addProductFilter($lastAdded);
                if (!empty($ninProductIds)) {
                    $collection->addExcludeProductFilter($ninProductIds);
                }
                $collection->setPositionOrder()->load();

                foreach ($collection as $item) {
                    $ninProductIds[] = $item->getId();
                    $items[] = $item;
                }
            }

            if (count($items) < 100) {
                $filterProductIds = array_merge($this->_getCartProductIds(), $this->_getCartProductIdsRel());
                $collection = $this->_getCollection()
                    ->addProductFilter($filterProductIds)
                    ->addExcludeProductFilter($ninProductIds)
                    ->setPageSize(100-count($items))
                    ->setGroupBy()
                    ->setPositionOrder()
                    ->load();
                foreach ($collection as $item) {
                    $items[] = $item;
                }
            }

        }

        $this->setData(\'items\', $items);
    }
    return $items;
}
}

app/code/local/MyCompany/Checkout/etc in config.xml:

 <?xml version="1.0"?>
 <config>
<modules>
    <MyCompany_Checkout>
        <version>1.0</version>
    </MyCompany_Checkout>
</modules>
<global>
    <blocks>
        <checkout>
                <rewrite>
                    <cart_crosssell>
                        MyCompany_Checkout_Block_Cart_Crosssell
                    </cart_crosssell>
                </rewrite>
        </checkout>
        <mycompany_checkout>
            <class>MyCompany_Checkout_Block</class>
        </mycompany_checkout>
    </blocks>
</global>

app/etc/modules in MyCompany_Checkout.xml:

<?xml version="1.0"?>
<config>
<modules>
    <MyCompany_Checkout>
        <active>true</active>
        <codePool>local</codePool>
    </MyCompany_Checkout>
</modules>

app/design/frontend/default/mytheme/layout/ in checkout.xml:

 <?xml version="1.0"?>
<reference name="content">
    <block type="mycompany_checkout/cart_crosssell" name="checkout.cart.crosssell" as="crosssell" template="checkout/cart/crosssell.phtml"/>
</reference> 

EDIT : To make the value selectable in the backend, you'll want to create:

app/code/local/MyCompany/Checkout/etc in system.xml:

<config>
<tabs>
    <mycompany_tab translate="label" module="mycompany">
        <label>MyCompany X-Sell Settings</label>
        <sort_order>100</sort_order>
    </mycompany_tab>
</tabs>
<sections>
    <mycompany_section translate="label" module="mycompany">
        <label>Max QTY For Upsell Block</label>
        <tab>mycompany_tab</tab>
        <frontend_type>How many</frontend_type>
        <sort_order>0</sort_order>
        <show_in_default>1</show_in_default>
        <show_in_website>1</show_in_website>
        <show_in_store>1</show_in_store>      
        <groups>
            <mycompany_group translate="label">
                <label>Settings</label>
                <frontend_type>text</frontend_type>
                <sort_order>1</sort_order>
                <show_in_default>1</show_in_default>
                <show_in_website>1</show_in_website>
                <show_in_store>1</show_in_store>
                <fields>
                    <mycompany_field>
                        <label>Maximum QTY To Display</label>
                        <frontend_type>text</frontend_type>
                        <sort_order>1</sort_order>
                        <show_in_default>1</show_in_default>
                        <show_in_website>1</show_in_website>
                        <show_in_store>1</show_in_store>
                        <comment>This is the maximum number of upsell products to display</comment>                    
                    </mycompany_field>
                </fields>                      
            </mycompany_group>
        </groups>              
    </mycompany_section>
</sections>    

Add this to your existing app/code/local/MyCompany/Checkout/etc/ in config.xml:

....
<adminhtml>
    <acl>
        <resources>
            <admin>
                <children>
                    <system>
                        <children>
                            <config>
                                <children>
                                    <mycompany_section>
                                        <title>MyCompany - All</title>
                                    </mycompany_section>
                                </children>
                            </config>
                        </children>
                    </system>
                </children>
            </admin>
        </resources>
    </acl>
</adminhtml>

And finally, you'd want to replace app/code/local/MyCompany/Checkout/Block/Cart in Crossell.php:

protected $_maxItemCount = 100;

With

protected $_maxItemCount = Mage::getStoreConfig('mycompany_section/mycompany_group/mycompany_field');

If you'd like to know why the config section works like it works, the best article for reference in my opinion is:

Alan Storm | Custom Magento System Configuration

Good luck!

I came across this looking for an xml way to do this and since @moose did the admin version I will share the xml way/

You will need to create a module to either extend or rewrite the checkout crossell block.

app/etc/modules/Namespace_Crosssell.xml

<?xml version="1.0" ?>
<config>
    <modules>
        <Namespace_Crosssell>
            <active>true</active>
            <codePool>local</codePool>
        </Namespace_Crosssell>
    </modules>
</config>

app/code/local/Namespace/Crosssell/etc/config.xml

<?xml version="1.0" ?>
<config>
    <modules>
        <Namespace_Crosssell>
            <version>0.1.0</version>
        </Namespace_Crosssell>
    </modules>

    <global>
        <blocks>
            <namespace_crosssell>
                <class>Namespace_Crosssell_Block</class>
            </namespace_crosssell>

            <checkout>
                <rewrite>
                   <cart_crosssell>Website_Crossell_Block_Checkout_Crossell</cart_crosssell>
                </rewrite>
            </checkout>
        </blocks>
    </global>
</config>

app/code/local/Namespace/Crosssell/Block/Checkout/Crosssell.php

<?php
class Namespace_Crosssell_Block_Checkout_Crosssell extends Mage_Checkout_Block_Cart_Crosssell
{
    public function setLimit($limit){
        $this->_maxItemCount = $limit;
    }
}

You can then simply add a setLimit action to your block <action method="setLimit"><limit>10</limit></action> like below.

Ideally you'd do this in local.xml like below

<reference name="checkout.cart.crosssell">
    <action method="setLimit"><limit>6</limit></action>
</reference>

or in a new block you can just add it in like below

 <block type="checkout/cart_crosssell" name="checkout.cart.crosssell" as="crosssell" template="checkout/cart/crosssell.phtml">
     <action method="setLimit"><limit>6</limit></action>
 </block>