You know, I am from the minority of people, for whom HoMM2 is the best in the whole series.
HoMM4 is close second. It is quite different from H2 or 3 and that's why plenty of people hate it. But it contains a lot of good ideas, like caravans or magic schools belonging to factions (life, nature, ...)
HoMM3 is for me just upgraded HoMM2, but it is a great game too. Changed inventory, great story, and others.

HoMM3.

HoMM3.

- Can't say anything about HoMM1, it's the only one i've never had, but it looks almost like a carbon copy of HoMM2 with less features.
- Graphic-wise, i always preferred the art style of HoMM2
- From a gameplay perspective, i think HoMM3 is the best af all
- I've found HoMM4 quite bad
- HoMM5 is a competent remake of the 2nd and 3rd chapter, but somehow misses the "magic spark" that the old ones have (also, has a worse user interface)

HoMM3.
I not usually hear the same about HoMM serie. For me -classic- opinions are :
HoMM1, too old nobody speak of it,
HoMM2/HoMM3/both, better game from the serie,
HoMM4, sucks,
HoMM5, good restart, takes HoMM3 but in 3D, keeping the few good ideas from HoMM4, but overall missing some magic from HoMM2/HoMM3.

HoMM5 is like HoMM3, except is not fun and is a corridor fest.

HoMM3
I was introduced to the HoMM2 demo myself actually :) Played it for countless hours at a friends house. I find the graphics nice and sweet, and the gameplay is very good as well.
It's just that HoMM3 looks a little better, technically at least, and has a tad deeper and better gameplay. To me it was HoMM2 with "that little extra". As far as I can see, it's flawless!
One of the better selling points in my opinion is the random map generator. With a couple of clicks you got a uniques map just for you. There are settings for size, difficulty, resources, monsters, pretty much everything. Makes the pick up and play experience even more convenient ;)
Once you install it on your school laptop though, you can wave those good grades goodbye D:

Absolutely. One of the best feature that keeps me addicted to this game.

HoMM3. Here's why.
HOMM1 and 2 both force you to drop unit stacks: you don't have enough room in your army to accommodate the different units you can buy from your castle.
HOMM4 is an inferior, buggier version of Age of Wonders.
HOMM5 could have been the best, but was rushed: it was incomplete, the campaigns lacked gravitas and weren't all given the same time as the first campaign (they gradually get weaker and less interesting as they go on) and there was the usual problems with massive amounts of bugs.
HOMM3 was a complete game. It wasn't perfectly balanced, but no game is - Starcraft needed 2 years of patching before it became "balanced" - but it was also more or less bug-free and the patches only fixed little exploits that people used, such as how many heroes you could buy from the Tavern that had random armies and so on.
HOMM3 all the way. WoG expansion pretty much completes it.

I started long time ago with King's Bounty, skipped HOMM1, got hooked on 2 and found paradise on earth in HoMM3. :)
So, HoMM3 is the best in the series, no doubt of it.
But I have been playing Heroes 2 again after all those years (never actually owned it before, I used to play it on my roomate's PC).
I must say, Heroes 2 has value on its own. It's much smaller, simpler game, good for playing in short bursts. Heroes 3 can drag you down sometimes, it's just too addictive.
But basically 2 and 3 are the same game. In a most positive way.
If you want to hook somebody on HoMM, let them play 2, and then destroy them with 3. :)

Guess it depends where you look. I've seen HOMM2 on lists of best games ever a few times. It regularly gets very fond responses when mentioned in the forums I've been to.
Absolutely. Incredibly good job, pretty much untoppable. 99% plus of my play was with the random map generator. Its robustness and variety was incredible.
FWIW, I got Disciples 2, which is very very similar to the HOMM series, and the single reason I no longer play it and am going back to HOMM2 (and maybe HOMM3 later) is that it is missing one of the most outstanding aspects of the game it imitates -- a good random map generator.

The short bursts part seems like an odd comment. You can make maps any size with HOMM2, including gigantic ones that would take weeks to get through. To me the hard part about the HOMM series is getting a short game in rather than a long one.

Heroes 2 is my favorite for everything aesthetic - I enjoy the music, the graphics, and the atmosphere better than any other Heroes.
Heroes 3, however, has the best gameplay and the most content (both fan-made and official).

Yous should play both either one of Heroes II/III and Heroes IV, which I find different in a good way.

My favourite would have to be HOMM3 because it is so accessible. I could virtually just start playing and still I am finding plenty of challenge in it. My second would actually have to be HOMM5. I am probably in a minority for liking this game but I think that it is actually a great return to the formula of HOMM3. It's just as simple to get into and it is the first Heroes game at least since the original to actually have graphics that didn't seem two years old at the time of release. HOMM4 is also a fine game. It just doesn't feel like Heroes to me and it has lost a lot of the simplicity that made HOMM3 a pick-up-and-play-game.The first to games I haven't played enough that I feel I can rate them.