The above is a reasonable specific mix, however you can also generalize it.
Generally speaking, a "balanced" party* wants...(* and not every quest needs a balanced party - but enough do that you might as well aim for it)
- a "Trapper"1
- a Healer2
- DPS3
- & some "at range" DPS4
& - Buffs5 (not "necessary", but always nice!)
And, of course, 1 character can easily fill more than one of those roles, and some can/should be filled by more than 1 character contributing. Both of these points are important when choosing a character/build - for instance, a "Ranger" can easily also be a Trapper, a Buffer, and a back-up Healer, so why not?...
There is also...
For those unclear on the concept, a "Tank" is a build that can waddle out and actively, intentionally attract attacks (aka "aggro"), so keeping the damage focused on themself instead of the party,
and withstand an absurd amount of damage that would quickly kill a non-tanky build.
Tanks are
not needed in most quests in DDO anymore, and a reliable tank is not easy to build.* Also, because Tanks focus so much on Defense, many Tanks do weaker damage, so 1) it takes a specific player who really wants to run one, and 2) they need/want to run in a party, because they don't have the DPS to do any sort of effective soloing (at best, soloing is slooooooowwwww.

)
(* Some builds are "tanky" or "tankier than others" (e.g. some (but not all!) Paladins or Barbarians), and can do "some" tanking with the help of a focused healer who concentrates on helping them survive. This approach requires good coordination/communication between the two players, if not the entire party.)
Bottom line - if no one is both 1) excited about it and 2) KNOWS how to build
and run one (or wants to learn), don't worry about it, you're fine without.
Notes:
1) "Trapper"
Almost any build can tweaked to be "a trapper"; all you need is 1 level of Rogue or Artificer, (swap-)gear (both +skill and +stat) that is current with your level, and enough Skill Points/level (on average!) to maintain the Trapper Skills:
- Spot*
- Search
- Disable Device
(* Spot is not necessary in 98% of quests if the trapper player knows the quests well, but some few quests have random traps!
Also, in a fixed party, it's possible for one character (perhaps a Ranger?) to have a high Spot and Search, and then for the actual Trapper to step up and do the work, so the trapper only needs the Disable Device skill - but this is a very specific arrangement. A good Trapper is self-sufficient, if at all possible.)
Note also that "Open Lock" adds a d20 to the roll, so, with good gear (Dex + Open Lock) and patience (to roll high), 90% (or more) of locks in DDO can be opened with just the 4 initial ranks. More ranks just make that happen easier/faster. Try to take your trapper class Level 1 for most skill points in trapping skills, but it's possible to "play catch up" for things like Iconic or uncooperative Caster/Trapper builds.
And it's never a bad idea to have 2 Trappers in the party, just in case one player is absent for a session or "the" trapper dies before the next trap.
2) "Healer"
In current DDO, very few quests demand a dedicated healer, one that has focused their Enhancements and Feats to that end. There are several reasons for this...
First, almost every class now has access to ~some~ sort of self-healing, and builds should lean toward this goal as a "good practice". That aside, any party of 5 can drag along a hire, and any combat-focused Cleric or Favored Soul can toss out enough Cure X Wounds to do the job, so anything more (a few Enhancements, or the lone Empower Healing feat) is ample. Also, lowbie casters can use Wands that offer higher level healing spells - handy.
Similarly, a healing-spec'ed Bard or Ranger could service as a semi-healer, and of course 2 (or more) are even better at picking up that slack.
Lastly, Raise Dead is important (and Resurrection at higher levels). Even without a Cleric/Favored Soul, any character w/ a good UMD score can scroll Raise Dead starting as early as Level 7, and scrolling Heal spells is common practice in mid-/later-Heroics. The ability to reliably Raise Dead (and then heal them up to full) asap is critical for a "balanced" party.
3) "DPS"
Damage per Second - handing out the hurt, fast and constant. So many different ways to do this, but usually broken down into the 3 main categories of Melee, Ranged, or Caster*. Some AoE (Area of Effect") is wanted in the party to take care of groups of trash, but some focused 1-target is also wanted for Bosses and other Big Targets.
(* Yes, casters can cast spells that have a "range", but "Ranged" is bows/crossbows/thrown weapons, while casters are specifically "magic". It's the in-game terminology, accept it.
)
In the end, DPS is DPS, no matter how it's delivered. However, a party is better with a wider variety due to some quests having X-immune/resistant monsters.
& 4) "DPS at range"
Also, some sort of attacks-at-range, whether Ranged or Caster, are desired - some quests demand killing stuff you can't just walk over and slap. (And, while any/every alt can pick up a Simple Weapon crossbow and plink away, you want a couple characters who can deliver high DPS downrange - that champion Shaman on the clifftop is gonna express his feelings in unmistakable fashion once you start killing him, so you want to get it done fast.
)
5) "Buffs" (optional, but nice!)
Buffs improve the entire party, boosting the overall DPS and survivability. Sometimes a buff can be the difference between success and a wipe (e.g Fire Resist and Resist Fire are critical in some quests), or just avoiding an annoying side fight (Invis for everyone!).
Bards are, no doubt, the best at this. Having a Bard in the party can add some good DPS (usually melee, but not always), a great selection of Buffs, including some unique Song effects, and Healing. A Bard could also be a trapper if they really want - freakin' Batman! 
Second probably come Rangers and/or Wizards. Clerics have some important buffs too, but not as many, and other casters tend to have too few spell slots for a lot of "Utility" spells, altho' if all a Sorcie or Warlock can offer is Jump, even just that is always appreciated.
So, in short, a party can be almost anything you want so long as you have these basics (mostly) covered:
- DPS (including at least some that can be delivered at distance)
- Trapping
- some Healing
- & (eventually) someone who can (somehow) Raise Dead
Done. Anything more is gravy.
Edit: Now, regarding "What builds can/do I/we use?", try the link below. The post is a bit old and some (but not all!) builds could be improved, so when/if you find one you like, post a question about it and you'll get advice/suggestions on how to bring it up to current standards, if necessary.