Some lasers are intended to be multimode. Far greater power output is possible with multiple modes than just one, but having just one mode gives the best quality beam.
As far as "changing modes" or mode-hopping, it can be caused by a variety of things, but most frequently it is caused by the laser cavity changing shape minutely due to expansion from heating. In solid-state lasers (typically the most susceptible to mode-hopping) this is referred to as "thermal lensing".
A great way to investigate laser modes is to pump some laser pointer crystals with a 808nm diode and see (by running the output through a magnifying lens) what kinds of modes you can get . TEM34 can be seen while doing this, along with most other modes. Typically, the bigger the crystals, the easier it is to get some nice multi-lobed patterns.