Rather than carry an entire spare, if you are going on an extended trip, pull the alternator at home and verify, clean, and lubricate as needed so that you start with a good unit. You should at that point be good for another 5 years. If traveling in extremely dusty places, or if you submerge the unit repeatedly, particularly in muddy water, you may need to take it apart and clean it in the field. Brushes are an obvious wear item but are easy to replace. Bushings or bearing are the next wear items but if clean and well lubed before you start, they are very unlikely to fail in the field. If you submerge in dirty water, clean the alternator when you can with water (unit turned off) to remove accumulated dust and debris. I have never had one fail in the field.
However, I have had an idler pulley fail in the field, and if you have a serpentine system, it is perhaps the one thing that no one ever looks at or thinks about. Some are constructed so that they can not be serviced, in which case carry a spare. If serviceable, carry a replacement bearing as these are generally available at a bearing supply or NAPA for only a few dollars. If the idler fails, all accessories fail with it including the water pump. I would consider the idler more important than the alternator in this regard.