Is it good to have 2 or 3 of any pet?

[Cheaptoad]

My Blighthawk has done so well in certain fights I just thought it couldn't hurt to have a few more.

Are there any pets that we should have multiples of?

[Durothar]

Probably the most common I see is Chrominius. There's a lot of strategies for Celestial Tournament that feature 2x Chrominius due to the probability of him getting killed early on from crits. Aside from the tournament I can't imagine much need unless you're serious about PvP or just need more pets to level/stone.

[Ilostmahbucket]

I have a P/P and P/S Nexus Whelpling (two P/P would be ideal) that I use all the time in both the menagerie and pet battles.
Mechanical Pandaren Dragonling comes to mind.

[Jerebear]

I find having multiple breeds (P/P, P/S, S/S) of the Anklerender and Kneebiter are a great boon in PvE. Being able to get off Black Claw + both rounds of Hunting Party is useful in some boss fights (like the new legendaries in 6.2) so making sure your Zandalari is faster than the enemy but trying to eek out as much power as possilbe is useful.

I do the same for other pets that favor speed since being able to back away from S/S to get a P/S sometimes makes the fight smoother while still being faster than the enemy.

[Sepsis]

Outside of the Celestial Tournament I don't think there is much need for most people unless you really like to min/max in PvE like myself. I keep a stable of multiple pets of different breeds for many current and possible future battles.
The Flayer Youngling has been a favorite of mine in addition to the Nexus Whelpling and the Zandalari raptors mentioned.

[Drudatz]

for pvp only if you wanna be an annoyence that gets his butt kicked anyway :p
aka 3 crows, 3 nexus drakes, 3 sun flowers, 3 elek plushies (dont laugh! if seen that in PVP! pet battle), etc

[Deadpoint]

A few pets that I've found myself using more than one on the same team in PvE battles are Jade Oozling, Nexus Whelpling and Kun-Lai Runt. I have duplicates of a few others either because I thought it might be nice to have more but never needed them or caught wilds of different breeds and never got around to decided which I would use. Others are just worth so little on the AH it's not even worth trying to sell them so I keep them in my collection for now.

I had doubles of Pandaren Water Spirit and Chrominius for bad RNG on the Celestial Tournament but have since sold them.

[Dakaf]

I have a few duplicate pets that I've leveled. If they have an ability set that is best for being slow, I'll use it with the P/P breed. With a speed ability set, I'll level the S/S breed.

Blackfuse Bombling is a good example. H/H for explode, P/P for armageddon.

Good luck!

[Sternish]

I own quite a few multiples of pets, almost entirely for the different breeds. There's a few exceptions, i.e. I use (2) S/S Bronze Whelplings vs Vesharr. But for PvP, just a couple of examples are Ore Eater, I have an S/S and a P/P. The S/S is the go-to but I have a few teams with a Dazzling Dance caster and with that I use the P/P.

Jademist Dancer is another. S/S and P/S. For PvP I almost always use the S/S, but if I know my opponent is going to be slower than the P/S or faster than the S/S (usually PvE tamers) then of course I'll use the P/S. There are a bunch more but the idea is just having more options for different scenarios and different teams, not necessarily running 2 or 3 of the same pet on a team.

[Gahtmilch]

For PvE, I have 2 each of the following for their utility in Celestial Tournament:

Pandaren Water Spirit
Chrominius
Mechanical Pandaren Dragonling
Lil Bling
2 x S/S Rabbits (does not have to be the same rabbit type)
2 x P/S Moths (does not have to be the same moth type)

It's a very big pain in the hiney to stop using proven combos if the RNG should kick in and kill your use-more-than-once battle pet(s) once you've begun the tournament. Any other pet I have more than one of is solely because of breed variance or rarity. I do have a few duplicates just because of their overall awesomeness (Kun'lai Runt, Flayer Youngling, Feline Familiar, Nexus Whelpling, S/S Crow, P/P Emporer Crab, and Emerald Protowhelp spring immediately to mind).

There may be an achievement for winning a fight with 3x Vengeful Porcupette. Even though I have three, I have never bothered to kill any teams using all three at once. I am not sure if this achievement actually exists in-game (I am not much of an achievement person).

In PvP there are many 2-3 identical pet common teams (3 x MPD, 2-3 Weebominations, etc.) I don't PvP, so someone who PvPs should likely give you an example of the most commonly encountered duplicates in PvP.

-Gaht

[Mvallas]

Recently I've been having GREAT success - with my All-Star team. And I mean that literally. All Iron Starlets. Dynamo, Dynamax and Dynamite!

Three Iron Starlets, all with Wind Up, Speedball, and supercharge.

There's a LOT of PVE and PVP application for this team-up.

PVE there's quite a few Menagerie fights I can destroy with no prob with those three:
Quintessence of Light (surprisingly!)
Stitches Jr
Elenor
The two warthogs
I'm sure there's a few others I'm forgetting ATM...

Likewise two iron stars can duo Jeremy Feasel at the DMF no problem. I've also used two iron stars to duo the trainer up in the mountains of Kun-Lai.

PVP wise I tend to win 2 out of every 3 battles it seems... of course the bane/nemesis of this troop are Elementals. Particularly pains are the Tiny Snowman and the Terroclaw Hatchling. Both of these can solo my entire starlete team no problem, so it gets annoying - especially as a lot of people have a Terroclaw Hatchling in their lineups >_<

On the flipside though, most everything else gets wrecked big-time! One particular guy started his fight with Xu-Fu, and in three rounds I killed him and he surrendered. What was great is I ran into him four times in a row later after perfecting another team, and managed to get my 5-in-a-row with all three pets alive achievment! It was total cheese to get it with that team (as rarely all three are ever alive at the end of a batte) - but hey, i'll take it!

I wrote in another thread where people were discussing how "OP" the new Graves pet is - and I have yet to encounter a team with Graves my Starlet trio couldn't take out easily. Particularly graves as I can kill him before my first starlet goes down no problem.