Best Fight in all of Dragon Ball

Cell vs Goku is my pick. I'm sleepy, so I'll keep it short. The fight was even, it did a good job of showcasing both of their powers and skill, and if it weren't for the plot Goku would've had Cell beat with his Instant Kamehameha.

If I only had three minutes to convince someone to watch Dragon Ball, I'd show them either Goku vs. Nikki and Ginger from Dead Zone, or else Goku vs. the Bio-Warriors from World's Strongest. These fights are beautifully drawn, well-choreographed, lightning-fast and have powerful hits. Barring that, I'd show them Goku and Beerus fighting through the city in Battle of Gods.

In the core DBZ, my favorite fights are always those between roughly equal opponents. There aren't very many:
1) Piccolo vs. 17
2) Goku vs. Cell
3) Goku vs. Kid Buu
4) SS Goku vs. Frieza
Technically, Android 16 vs. Imperfect Cell is one, too, but it's not that visually interesting.

Cinematically, I think Goku vs. Frieza is the best battle for the reasons Beerus the Wondercat mentioned. It's got lots of twists and turns, as well as fun strategies and a boatload of epic moments. If only there was some way to trim it down from 4 hours long so you could actually, y'know, watch it in one sitting.

Goku's first Kaioken x3 on Vegeta, though, is pretty epic and fast, and the beam struggle afterward is still hype to this day.

A lot of fights I used to love, like Gohan vs. Cell, are kinda boring now that I understand how one-sided they are.

1. Goku vs Piccolo

Even though Piccolo doesn't have all the special techniques yet that he'll get later on in DBZ like the SBC or the Hellzone Grenade, still a very interesting fight with lots of good old-fashioned beatdowns to supplement the techniques, rather than just ki blasts and powering up and transforming everywhere.

2. Piccolo vs 17

- Piccolo's last great fight all the way up to when he fought Frost in DBS. Also gives us the Hellzone Grenade. Also not a single blond haired fighter in sight (not counting #18), as this is the point where Super Saiyans first started entering Bargan Sale levels.

3. Goku vs Cell

- Visually interesting fight, lots of techniques on display. Cell playing around with Goku allowed him to show off old favorites and combo them together, like Tien's multiform with a quadruple Special Beam Cannon. Also gave us the Warp Kamehameha, which had everyone from the villain (who is part Goku and knows how he thinks) to the archrival to the best friend to the son all freaking out thinking Goku had snapped and was about to destroy the planet.

4. Majin Vegeta vs Goku

- Another great fight, this one with the extra benefit of having some emotional weight. Vegeta's betrayal of everyone for the opportunity for more power just to settle his grudge all while the fight feeds the slumbering Majin Buu was pretty awesome. Dragged down slightly when we realize later that Goku held back, much to Vegeta's anger.

5. Roshi and Goku's fights with the Biowarriors.

- As others have mentioned, very beautifully done.

Honorable Mentions:

- Piccolo vs Frost. A complete mismatch of a fight where only Goku's fight prior to this even gave Piccolo a chance by wearing Frost down a bit. Had Frost not cheated, Piccolo would've defeated a far superior opponent through planning and strategy.

- Broly's beatdown of the Z Fighters in his first movie. The scene where he clotheslines Gohan and Trunks and simultaneously kicks Piccolo still looks awesome.

Agree agree agree! Of the three arc-finishing fights (Goku vs. Frieza, Gohan vs. Cell, Goku vs. Kid Buu) I'd say Gohan vs. Cell is the least exciting, and for the reasons you described. Half the time, Gohan doesn't want to fight, and the other half of the time he's just messing with him. Goku vs. Cell is more interesting. I will add, though, that Gohan vs. Cell's Kamehameha battle is probably the most intense, desperate moment of Dragon Ball. So on the whole the fight's pretty lame but it's got the best finisher of all DBZ.

Also gotta agree with @skar : Vegeta vs. Recoome is awesome. For some reason the art quality is a lot higher than the fights before and after on Namek, and it's probably the only time in DB where one opponent is way stronger than the other but still gets the crap beat out of him. I've shown this fight to a few non-DB fans before, and they usually get completely sold about here:

Possibly the most beautiful moment of DBZ.

I don't like Gohan vs Cell that much, it was cool in terms of visuals and themes but it felt too one-sided in the end. Do like these, though;

1. Goku vs Frieza
2. Goku vs Vegeta (first fight)
3. Vegito vs Fused Zamas
4. Vegito vs Buu
5. Vegeta vs Cell (before and after he reaches his perfect form, mostly because of the emotional side of it)

Despite me loving Vegeta, but he really screwed up a potential epic even fight between those two. That or Akira being a lazy bastard. XD

SSGSS Goku V Golden Freeza.

I agree with this. It really wasn't much of a fight.

Now, the buildup to that moment I think is what everyone likes, and perhaps seeing Cell finally get his comeuppance, but the actual blow-for-blow fight itself wasn't that stellar without any type of emotional connection.

Based on the posts so far, either Goku vs Frieza or Goku vs Cell are everyone's favorite fights with Gohan vs Perfect Cell being their least favorite. Truthfully all three fights are great in their own ways since they offer something spectacular that the other two cannot bring to the table. The Frieza fight was simply a brutal slaughterfest that was well balanced almost throughout the entire duration that had a healthy climax on a dying planet. The Gohan fight was superb in being a magnificent one-sided beatdown in contrast to all of the other balanced fights in the series. Plus the kamehameha clash was well done. The Cell fight against Goku was also good, but is the weakest of the three despite having some badass moments.

Cons:

1. Very slow start up (honestly both fighters were simply playing around for like the first 10 minutes that had no tension. Only when they powered up was when it got interesting, especially when Cell blew up the arena).

2. Constant Hercule and Firecracker commentary.

3. No Spirit Bomb (would have been dope if both fighters created a genki dama to overpower the other in energy created from either pure or negative energy).

4. Goku giving up (Even though it was almost guaranteed that Goku would have lost if he reengaged against Cell, but it would have been epic in some manner since it is well... Goku we are talking about. I would have loved it if Goku fired a Super Kamehameha while using the super kaioken to severely damage Cell while dying in the process. With his sacrifice fresh on everybodys mind, Gohan instantly becomes a SSJ2 with Cell receiving no senzu bean, thus making his beatdown even more brutal with the extra passion Gohan is giving him. After all if Goku was planning to die anyway in this arc, mind as well be in action while also being the one personally responsible for his sons ascension).

Pros:

1. Balanced fight (The fight went constantly back and forth despite Cell not even using anywhere near his full power. Nonetheless Goku went far to the point he managed to drastically make Cell's ki drop during the climax of their fight).

2. Good Z-Fighter commentary (especially from Vegeta and Piccolo).

3. Multiple techniques being utilized.

4. Reminiscent moments (This fight felt like Goku fighting against Frieza in certain moments when Cell used the tsubi kienzan or when they gripped locks against each other. Good times indeed).

5. Music (despite the lack of certain silent moments or that one track that liked to play when the tension died down, it was relatively a good addition to the fight by Bruce Faulconer).

So ultimately the Goku vs Cell fight is good, though it does have its flaws. Granted the Frieza and Gohan fights are not perfect either, but the Goku and Cell flaws are more noticeable (at least to me) compared to the other two. Granted all three are fantastic, so either way you will get a enjoyable experience whether you want to watch the Freiza (four hours), Gohan (over two hours), or the Cell and Goku match (over a hour). 

With that being said, I still say that Goku vs Majin Vegeta is the best fight though it is my subjective opinion on the manner.