Way to de-level yourself

Followers have stats just like the player in skills and health. Those values are static and are set the first time you enter/load the zone that they are in. There are also maximum level caps for followers should your level be higher than that the first time you encounter them.

For example, most people meet Lydia very early on and she'll end up being locked in with 100 health and skills in the 20s, so she won't be as effective as Jordis (the housecarl you get in Solitude) whom you'll usually meet much later on since the house costs 25k gold to purchase.

If you are on the PC, there is a way to force an NPC to level up by resetting them:

1. First, remove all the gear from the follower (at least the ones that you want to keep).
2. Walk up to them, be as close as possible, open the console with the ~ key
3. Click on your follower. When you do so, a string will appear at the top of your console that represents your follower's reference ID.
4. On your console, type disable, then follow it up with enable

After this, your companion will be 'reset' to match what your current level is. Their health and skills should be improved.

Finally, keep in mind that all followers fall under a general category: warrior, thief, or mage. Lydia, for example, is a warrior and will never gain a sneak skill above 15 no matter what level you meet her at.

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.