How to find MongoDB index statistics
You can get overall (instance wide) hit info from the db.serverStatus() command, and in particular:

http://docs.mongodb.org/manual/reference/command/serverStatus/#serverStatus.indexCounters.hits
http://docs.mongodb.org/manual/reference/command/serverStatus/#serverStatus.indexCounters.misses

These numbers are totals seen for the lifetime of the process, so if you want to get a rate or see the trend over time, then you will need to record them periodically and diff the values accordingly.  Thankfully, if you install MMS Monitoring, it will do that for you and graph the results.

However, there are currently no per-index statistics available.  The relevant feature request can be found here for tracking and voting purposes:

https://jira.mongodb.org/browse/SERVER-2227

Update: January 2016

The stats referenced above have been removed from the output of the server status command, so are no longer available.  However, the referenced feature request is now complete and is available in version 3.2 in the form of the $indexStats aggregation operator (the linked docs also contain sample output). For completeness, here's an example I put together:

Prior to any queries I have just 2 indexes, the default _id and indexme, both with 0 ops:

&gt; db.foo.aggregate( [ { $indexStats: { } } ] ).pretty()
{
    "name" : "indexme_1",
    "key" : {
        "indexme" : 1
    },
    "host" : "localhost:27017",
    "accesses" : {
        "ops" : NumberLong(0),
        "since" : ISODate("2016-01-12T19:03:01.358Z")
    }
}
{
    "name" : "_id_",
    "key" : {
        "_id" : 1
    },
    "host" : "localhost:27017",
    "accesses" : {
        "ops" : NumberLong(0),
        "since" : ISODate("2016-01-12T18:59:24.292Z")
    }
}


Then run a couple of finds to bump the ops on indexme and check again:

&gt; db.timecheck.find({indexme: 33})
&gt; db.timecheck.find({indexme: 55})

&gt; db.timecheck.aggregate( [ { $indexStats: { } } ] ).pretty()
{
    "name" : "indexme_1",
    "key" : {
        "indexme" : 1
    },
    "host" : "localhost:27017",
    "accesses" : {
        "ops" : NumberLong(2),
        "since" : ISODate("2016-01-12T19:03:01.358Z")
    }
}
{
    "name" : "_id_",
    "key" : {
        "_id" : 1
    },
    "host" : "localhost:27017",
    "accesses" : {
        "ops" : NumberLong(0),
        "since" : ISODate("2016-01-12T18:59:24.292Z")
    }
}