Which followers are a different level than the Dragonborn

So here's what I know you can do (name followed by the quest you should start but not complete):

People

• Any normal follower (or, hey, Aranea Ienith can summon an atronach)
• Delphine + Esbern - Alduin's Wall (Esbern can summon an atronach)
• Brother Verulus - The Taste of Death
• Mercer Frey - Speaking with Silence
• Thonnir - Laid to Rest
• Avulstein Grey-Mane + Geirlund + Vidrald - Missing in Action (the latter two should join you and Avulstein at Northwatch Keep)

Animals

• Meeko (Meeko's Shack) or Stray Dog (random encounter)
• Barbas - A Daedra's Best Friend
• Horse (better yet, Shadowmere)

Summons

• Two summons (with 100 in Conjuration and the Twin Souls perk). Some dead thralls can summon atronaches, so that gives your summons one summon apiece.

which brings the total to you, nine people, two dogs, a horse, two dead thralls and four atronaches. That's 13 permanent and almost everywhere (excluding atronaches and the horse) and 18 potential. This seems pretty hypothetical and I haven't done it myself, so feel free to correct me.

Other

There's also supposedly a glitch (patch status unknown) where you can dismiss your follower, hire someone else, then immediately return to your follower and rehire him or her. I don't know if people use it with the Dark Brotherhood Initiate(s) for a reason or because it only works with them.

Also Odahviing.

Yes, you may absolutely use a strong and powerful Lydia for the entire game. I'll explain below.

Problem

As mentioned in the other answers here, the game locks followers around the level you are when you acquire them. Because of Lydia's typically early acquisition in the game, she is leveled extremely low and will become useless if nothing is done while you become stronger.

EDIT: As of patch 1.6 this problem has been fixed. However I am not positive if the fix affects current saves, so this solution may still need to be used for your currently under-leveled followers from games started pre-1.6

Solution

The Wabbajack - A staff granted for completing the Daedric Quest: The Mind of Madness

The quest is extremely easy and doable at any level. You must have access to Solitude. I'll let you do your own research on the quest itself. To the point:

• Important: Release Lydia from your service first.
• Use the Wabbajack on Lydia until she morphs into a another creature: A goat, bunny, daedra, whatever. It's important that she morphs.
• Use the Wabbajack again to morph her back. If she returns wearing her default armor, the attempt has been successful and she will be re-leveled to your current level.
• Re-hire Lydia as your follower.

Why? The act of morphing her to another creature, and then morphing her back resets her stats to your level. Yay.

Notes

• Defintely quick save or save before attempting to use Wabbajack on Lydia. The wabbajack is random and has many effects including Instant Death.
• Take any rare items from her before the transformation attempt, as she sometimes loses them on her return to a human state

That's it. I've put in over 200 hours in Skyrim and I've had Lydia the entire time. Currently on Master @ level 55 and Lydia is basically her own demi-god. Have fun.