Yes
Targeting Yourself
If a spell targets a creature of your choice, you can choose yourself, unless the creature must be hostile or specifically a creature other than you.
(Player's Handbook p204)
In the case of Greater Invisibility, the caster is specified as an additional target to clarify that the caster is a valid target even when the caster cannot be touched (if she were manacled against a wall, for instance). Ordinarily, a spell which only targets "a creature you touch" (such as Cure Wounds or the standard Invisibility spell) cannot be used on any creature that cannot be touched.
What exactly qualifies as "touch" is not precisely defined in the rules; however, the text of Greater Invisibility in particular suggests that touch is not automatic against oneself.
Targeting the same creature multiple times simultaneously with the same effect causes the creature to be affected still only once
That is, this GM would rule that just because an effect can be used one time against multiple targets doesn't mean that the same effect can instead apply multiple times against one target and yield multiple results.
While it can be technically lawyered that a spell that affects multiple creatures can, instead, affect the same creature multiple times, that notion doesn't yield positive results in actual play (i.e. you'll earn a book to the noggin not applause). And, as you can see from broaching the question here, even bringing up the idea is anathema to some.
To put this negative reaction in perspective, let me employ an analogy: a game show contestant is allowed to pick two cars. While most contestants will pick two different cars, this contestant baffles host and studio audience by picking the same car twice, technically picking two cars: this car and this car again. Although this impresses the game show's lawyers, and the sponsor's pleased at the prospect of only having to provide one vehicle, this makes for lousy ratings. Seriously, don't do this: you don't want to make Drew Carey—or the GM—angry.
That said, the spell mass cure light wounds targets "one creature/level, no two of which can be more than 30 ft. apart." However, once the caster has picked that one creature to be affected, picking that same creature likely runs afoul of of Combining Magical Effects: the creature is supposed to realize simultaneously enough the same spell's effect multiple times, something the game usually either rejects outright or accommodates grudgingly (by mandating only the most recent, most beneficial, or most detrimental effect occurs).
With that in mind, a GM could allow a lone creature to be targeted multiple times by a mass cure light wounds spell then have only the highest individual result affect the target… or even have the target affected uniquely only once, the GM mandating all creatures that the spell would've affected would've been affected equally.
Compare the spell mass cure light wounds with the spell wail of the banshee: the wail targets "one living creature/level within a 40-ft.-radius spread," and "[c]reatures closest to the point of origin are affected first." This does not mean if a Wiz20 catches but two creatures in that 40-ft.-radius spread, the wizard can force those two creatures to make 10 successful Fortitude saving throws each or die! Each affected creature instead makes 1 saving throw, and the remainder of the spell's effect is wasted. (By the way, here's a Paizo messageboard discussion about the spell wail of the banshee.)
This GM urges that unless a spell or effect says otherwise, a decision to use the spell or effect against less than than its maximum number of targets doesn't make the spell or effect's power greater against the targets the spell or effect is used against!
(I could find but this lone 2011 Paizo messageboard thread discussing the idea of picking the same target multiple times for an effect that affects multiple creatures. The topic doesn't seem to warrant serious consideration.)
Best Answer
I asked Jeremy Crawford the same question and they clarified the situation with this tweet:
In your example, spells like Thunderous Smite or Wrathful Smite could be made to also affect the caster's beast companion through the Share Spells feature of the Beast Master. However, Thunderwave would not work because it is an area of effect spell and thus it lacks a target.