Carl, referen the links bellow to get a good understanding on the industry standard STP ( 802.1D project ),
this is a very extensive question. once understood you will see a better picture down the road on other types of Cisco proprietary
Spanning tree versions and flavors.. but stp is basically a link management protocol, as well as used to prevent bridging loops in a network. See bridging loop links bellow for details. Link management is where dual paths exists from one switch to another
to provide link redundancy.
STP as Layer 2 protocol
http://global.zyxel.com/support/supportnote/ves1012/app/stp.htm
STP timers, go through this document which can explain in more details the scope ot STP timers, STP timer values are set by default , however, values can be changed to obtain faster STP converging in its management throughout the stp topology.
http://www.cisco.com/en/US/tech/tk389/tk621/technologies_tech_note09186a0080094954.shtml
STP should be used on two or more catalyst switchs.
Configuring and Building spanning tree topology
http://www.cisco.com/en/US/docs/switches/lan/catalyst2950/software/release/12.1_6_ea2c/configuration/guide/swgstp.html#wp1019959
Your question on " When will networks start seeing Spanning tree issues " I think you are referring to bridging loops. The concept of spanning tree issues or spanning tree loops has been missed used for years, it should be instead bridging loops issues, in any case, here is when STP protocol comes in place to prevent these loops and ease our lives.
refer to this link for understanding bridging loops in a network.
http://www.cisco.com/en/US/tech/tk1330/tsd_technology_support_technical_reference_chapter09186a00807597b8.html#wp1021881
HTH
Jorge
Jorge Rodriguez