As you know, Gourry travels with a very lively crew of companions throughout the series. Let's take a moment to analyze his relationship with each of them:
Lina Inverse - Lina, for the most part, prefers to shield her emotions for Gourry rather than openly declare her appreciation. But I think that we all know the truth about these two. ^^; They are perhaps the most inambiguous, perfect pair in all of Slayers; they coincide each other's lifestyles (and appetites o.o) flawlessly, even though neither of them seems to be very good at admitting it. Anyway, I believe that Gourry is far more than Lina's "sidekick." In a sense, he is also her "better half," her "guardian," and her "shoulder to lean on."
Zelgadis Graywords - In terms of personalities, Zelgadis and Gourry are complete opposites. (And no, I don't mean that Zelgadis is smart and Gourry is stupid. O.o;) Zelgadis is extremely motivated (almost eccentric, to a degree) on finding a cure, whereas Gourry could not possibly be more outgoing and at ease. Knowing this much, it is rather easy to see that they often do not support each others' goals, and that their lifestyles contrast to the point of near-opposites. However, they are both reasonable men, and they accept each other -- no matter how eccentric/dense the other may seem. ^^;; So, I guess you could say that Zelgadis and Gourry get along pretty well.
Amelia Wil Tesla Saillune - Out of the entire gang, Amelia is probably the most tolerative towards Gourry's denseness. She never hits or reprimands him when he makes a dumb comment, so I suppose that you could say these two are on a pretty good basis. ^_^ However, they very seldomly interact with each other.
Sylphiel Nels Rada - *sigh* Poor Sylphiel. She has nearly devoted her life to chasing after her hopeless love, Gourry, and he hardly even notices her. -.- Some people view it as a beautiful and depressing love story; others see it as an annoyance. But no matter what the opinion of the fan may be, I think that it is rather evident that Sylphiel is very compassionate towards her dear Gourry. Sadly, he won't ever return her feelings.
Martina Zoana Mel Navratilova - Martina was once infatuated with Gourry, which doesn't come as much of a surprise, considering that she's fallen for every male in Slayers at one point or another. But other than that meaningless little "crush," these two are oblivious to each other. Martina "got over" Gourry in a very interesting way; she was so taken aback by his denseness that she vowed never to love again. This vow, like all of her other ones, did not remain true for very long. o_O
Xelloss - Xelloss always seems to have a bag of tricks up his sleeve (which justifies why "Trickster Priest" is such a fitting nickname for him), and he just loves to tag-a-long with the group while delivering his clever pranks. However, he pays little attention to Gourry, who always takes things far too literally to understand Xelloss' pranks. Every now and then, Gourry's blunt comments earn an effusive face-fault from Xelloss -- but that is basically the only interaction that takes place between these two. ^^;;
Filia Ul Copt - Due to his perpetual denseness, Gourry has given Filia the impression that he is pervert. o.o; (Even though he's not.) They interact quite often -- If you've ever witnessed a typical scenario between these two, then you'd know what a funny pair they are. ^^ Whenever Gourry lifts up Filia's skirt (out of curiosity for her tail, and not out of pervertedness), Filia always whacks him with her mace in self-defense, and sends him flying through space in a "pinball" sequence. Now, that's comedy!
Zangulus - Well, I suppose that Zangulus and Gourry don't exactly qualify as "companions," but nevertheless, I just had to put him here. ^_^ Why? Because even though Zangulus has tricked himself into believing that he is an enemy to Lina and Co., he often aids them because he has a good heart. Either way, his talent with the Howling Sword rivals that of Gourry, whom he challenges at every opportunity. But in the end, Gourry is still a better swordsman than Zangulus. ^^;