Are champion-specific rune pages needed in order to be competitive?

Generally, rune pages can be shared by multiple champions. There are times though where rune pages can be extremely effective when they are made for a specific champion.

Standard AD Page: AD Marks, Armor Seals, MR Glyphs, AD Quints/Lifesteal

Ezreal AD Page: AD Marks, Armor Seals, Mixing MR Glyphs with Mana Regen, AD Quints

Standard AD Jungler: AD Marks, Armor Seals, Scaling MR Glyphs, AD Quints

Nocturne Jungler: AS Marks, Armor Seals, Scaling MR, AS quints

Standard AP Tank Top: Hybrid Marks, Armor Seals, MR Glyphs, AD/AP Quints

Mundo Top: Hybrid Marks, Armor Seals, MR Glyphs, HP/5 Quints

Ryze Top: Hybrid Marks, Armor Seals, Mana Glyphs, Mana Quints

Notice that a the standard pages, multiple champions can use. Some champions work very well with specific rune pages though which gives them a nice advantage in lane.

Ezreal tends to be very poke heavy and can run out of mana fairly quickly if you poke hard. Adding some Mana regen in place of some MR can win you the lane by letting your extra poke whittle down the enemy forcing them to either play defensive or potentially die.

Many junglers like Pantheon or VI build straight AD for damage from abilities. Some junglers synergize very well with the new Feral Flare or do more damage overall the faster they attack and so instead of damage building lots of attack speed greatly increases their damage output.

Many top laners will have pretty similar builds. Some tanky ones like Malphite or Shen might run those standard pages I show up top. Other tanks like Mundo don't benefit from the same. Mundo tends to farm with his cleaver which constantly drains his HP. He needs the extra health regen quints to safely farm from afar to keep his HP up. Ryze gets a huge bonus from having extra mana to damage. Level 1, if you have all mana Glphys/Quints can get his level 1 spell damage to 109. This is pretty significant.

Basically, you don't NEED to have additional rune pages. You can get away with having 2-5 but if you are vs a similarly skilled player, your better runes could give you the edge to win the match and potentially snowball your lane. Currently, I run 19 rune pages for a variety of champions.

Having a perfect, specialized set of runes can sometimes give you a tiny advantage in a lane/game. However, the lane/game is overwhelmingly determined by your skill with the individual champion first, and champion matchups second. Runes are a tertiary factor at best, and it requires a pretty high skill level for this to really be a relevant issue.

Therefore, you can get by for a long time with generic runes on the vast majority of champions. If you have a lot of IP sitting around, you can spend some time thinking about idealized runes and whatnot, but if you don't have the IP, I wouldn't spend much time worrying about it. Even in, say, platinum level play, you don't need that many rune pages.

You can get away with 5 pages minimum (basically one for each role), but having about 7 is a slightly safer number (to cover the possibility of facing an AD mid or an AP heavy top). From there you can build specialized pages for specific champions.

I know this thread has been answered already but still, my view on this... Some champions can share rune pages like described above. However, some champions require a personal rune page depending on how you play that champion. For myself, I have a special rune page (and masterie page) for my Ezreal. I play Ezreal like noone plays him, but it works for me. I play it with AD quints, AD marks, flat health seals and CDR glyphs. This gives me 10% CDR but then I would have no magic resistance. Therefore I replaced the nerfed armor seals with flat health. For me, this is the perfect balance, but it's a pretty weak start build.

It all depends on how you play basically. Some people like to have AD marks on mages mid to be able to last hit better and to have a bit more harass early game in laning phase, but not everyone likes that.

So basically: you should stick with a few champions and master them so you know whether to use specific rune pages or not :).