Let's take some common routing protocols in use today:
EIGRP -- uses a combination of bandwidth and total delay (also by default a function of bandwidth). EIGRP can optionally use other criteria, such as load, reliability and MTU size, but in 99.9% of networks, these are not used.
OSPF -- uses a single metric. In the Cisco world, it is bandwidth.
BGP -- Everything else being equal, BGP uses hop count, but for BGP a "hop" is an entire autonomous system.
Since IS-IS seems to be making a comeback, I'll include it as well. IS-IS uses an static administrative metric. In other words, the metric is whatever you set it to.
Link utilization and other "transient" values cause more problems than they solve. And in modern networks, it just isn't important enough to bother with.
Note that these are the default values. You as the network administrator can change them to suit your needs. BGP in particular is designed to allow more administrative control over the path selection.