If you enable Info:Simple logging (still applies at 10), process IDs get put in your server log. You can view the logs via server manager or you can go to C:\Program Files\ArcGIS\Server10.0\server\user\log and dig through the .dat file. Here's a excerpt from my dev machine:
<Msg time='2010-12-01T12:18:43' type='INFO1' code='3007' target='Server' thread='5960'>Attempt to start configuration maps/stuff of type MapServer.</Msg>
<Msg time='2010-12-01T12:18:44' type='INFO1' code='17004' target='maps/stuff.MapServer' methodName='GraphicFeatureServer.Construct' machine='blahblah' process='9276' thread='4168'>GraphicFeatureServer Construct started.</Msg>
<Msg time='2010-12-01T12:18:44' type='INFO1' code='17002' target='maps/stuff.MapServer' methodName='GraphicFeatureServer.Construct' machine='blahblah' process='9276' thread='4168'>Default Map name is: Layers.</Msg>
<Msg time='2010-12-01T12:18:44' type='INFO1' code='17002' target='maps/stuff.MapServer' methodName='GraphicFeatureServer.InitializeLayers' machine='blahblah' process='9276' thread='4168'>Layer Initialization Summary. Layers in Map: 2. Successful Initialization on: 2. Unsupported Layers count: 0. Failed Initialization on 0.</Msg>
<Msg time='2010-12-01T12:18:44' type='INFO1' code='17002' target='maps/stuff.MapServer' methodName='GraphicFeatureServer.Construct' machine='blahblah' process='9276' thread='4168'>Initialized 2 Layer(s).</Msg>
<Msg time='2010-12-01T12:18:44' type='INFO1' code='17002' target='maps/stuff.MapServer' methodName='GraphicFeatureServer.Construct' machine='blahblah' process='9276' thread='4168'>Initialized 0 Table(s).</Msg>
<Msg time='2010-12-01T12:18:44' type='INFO1' code='17006' target='maps/stuff.MapServer' methodName='GraphicFeatureServer.Construct' machine='blahblah' process='9276' thread='4168' elapsed='0.01660'>GraphicFeatureServer Construct ended.</Msg>
<Msg time='2010-12-01T12:18:44' type='INFO1' code='12002' target='maps/stuff.MapServer' methodName='KmlServer.Construct' machine='blahblah' process='9276' thread='4168'>Construct started.</Msg>
<Msg time='2010-12-01T12:18:44' type='INFO1' code='12003' target='maps/stuff.MapServer' methodName='KmlServer.Construct' machine='blahblah' process='9276' thread='4168'>Construct ended.</Msg>
<Msg time='2010-12-01T12:18:44' type='INFO1' code='3013' target='maps/stuff.MapServer' thread='5960'>Configuration maps/stuff.MapServer is started.</Msg>
Process ID 9276 corresponds to the ArcSOC.exe for this map service.