As far as I know data you want is not available on SNMP.
3750#sh mls qos interface FastEthernet0/1 statistics
...
output queues dropped:
queue: threshold1 threshold2 threshold3
-----------------------------------------
queue 0: 0 0 0
queue 1: 100989 0 0
queue 2: 0 0 0
queue 3: 0 0 0
...
What you'd like to know is ifIndex, queue, threshold and drop counter. I'm not aware of populated MIB/OID where these values can be polled from.
Like John Jensen explained, outDiscard is only thing you can get, but it aggregates all of this, so you won't know if it's BE, AF, EF, NC or what, which is dropping. You probably wouldn't care about BE drops, but you'd care about EF drops.
There are two OIDs where these aggregate egress drops are stored, if your ifIndex is 10001, you'd find them here (symbolic and numeric presentation):
IF-MIB::ifOutDiscards.10001
.1.3.6.1.2.1.2.2.1.19.10001
EtherLike-MIB::dot3StatsDeferredTransmissions.10001
.1.3.6.1.2.1.10.7.2.1.7.10001
3750/3560 are not very good switches for application which can microburst, i.e. if your egress is 1GE and ingresses are 1GE too, two very low average rate ingress ports can easily congest the egress port, causing drops. To maximize the available buffers (and minimize microburst drops) follow this document.
Try to disable it with the right-to-use license:
Switch# license right-to-use deactivate ipbase all
Switch# reload
Best Answer
Mostly, modern switches don't increase latency; they switch are wire speed, since most of it is done in hardware. Buffering traffic slows it.
Switches tend to have very, very small buffers. The reasoning is that it is better to drop traffic early than to slow it down. Networks prefer that any traffic which will be dropped be dropped as soon as possible (if a switch must buffer traffic, it is likely to be dropped by subsequent network devices) to give a head start to detection and retransmission.