How necessary are certain team positions?

[DarkmasterChaos]

I'm a person who sucks at making teams... I mean I'm a guy who puts together a team of sweepers only. But that isn't the point.. I want to know how necessary are certain roles.... Really? How necessary? The roles I wonder about are the following:
Clerics (Pokemon with Heal bell or Aromatherpy)
Hazers
Psuedo-hazers
Toxi/pyro/parashufflers
Any annoyer

How necessary are these guys? I mean for a competitive team.... Which ones do you really want to use? And another question of mine is what roles must your team have to be competitive (I.E You can live without a Cleric but you MUST have a sweeper of some sort on your team(In most cases)). Eh and if I can ask one more.... What moves should every team have (I'm referring only attack moves I.E Everyone should have 1 pokemon with EQ and Ice beam etc.) Thank you (in advance) for your time and patients.

[PhazonElite]

Well, clerics are by no means needed, neither are hazers. However, if you don't have a hazer, its a good idea to use a psuedo-hazer. Hence the reason skarmory is so good. A toxicshuffler, spiker, psuedo-hazer all-in-one is just amazing.
One annoyer is usually a great thing, but they aren't neccessary.
The majority of any team is usually sweepers though.

[rctan9]

A lot of pokemon can "multi-task" as several roles. Just add Toxic and Rest onto [insert name of sweeper] and you got yourself an annoyer as well.

[Kuiper]

Rapid Spinners are a good thing to have in a Spike heavy environment. Hazers are also good if you have no other way to negate stat boosters (I onced use Psyche Up and Baton Pass to peudo-pseudo Haze).

It's usually a good idea to have a physical and special sweeper, so you don't die to a wall (Regice, Skarmory) and a mixed sweeper is good for defeating the Skarm-Bliss combo.

It really depends on your metagame and your team, if you're using Shedinja, a Rapid Spinner is a must.