Have you been fertilizing every spring and fall? Other than that, not too much you can do besides spread the out if they are too crowded. And if they do flower, when the flower is done, cut if off, don't let it waste energy going to seed.

I've also heard it recommended not to water them after they bloom, at all. This discourages the bulbs from splitting, so it slightly raises the rate of reflowering the next year but that's only for ones that bloomed in the current year.

For sure move the too shaded ones. When you dig mix bonemeal in the lower soil. I would probably also add a low nitrogen fertilizer like bulb food.

When I lose tulips here in warm winter zone, no foliage.

Here's a protocol that works for me:
When planting, the more sun the better.
If the soil is in relatively good condition (other perennials grow well), don't bother fertilizing.
When the foliage begins to yellow or has yellowed completely, dig the bulbs. (keep colors seperate if you don't want the yellows and reds to dominate!)
Spread them out somewhere dry to cure(dry out completely) for a couple days.
Break off the old roots and stems, seperate out the larger bulbs, throw the rest in the compost.
Store them in a warm dry spot in something that won't hold moisture (mesh bag, paper bag, open trays)
Replant in early fall.

Just dividing and keeping them dry over the summer might be enough to bring on extra blooms next spring.

Kato b, your suggestion just might work and, as far as I'm concerned, is worth the risk since most of these babies aren't budding and flowering anyway.

Fertilizing and overcrowding were never the issues, IMO.

It may be too, that the non blooming ones are just not the more perennial ones, and you may never have good luck with getting them to reliable bloom.

If the suggestions above don't work, I'd pitch them and going forward only purchase perennial ones.

Sue

Aren't all tulips perennials? Never heard of annual tulip bulbs.

Aren't all tulips perennials? Never heard of annual tulip bulbs.
Though a lot of tulip packaging and descriptions might lead you to believe they will provide you with years of beautiful spring blooms, that is often not the case. Most tulips will only bloom nicely the very first spring, and after that, there will be foliage emerge, but very few blooms, and thus be a real disappointment.

Darwin Hybrids usually bloom well for several years and even multiply.
Other good choices for reliable spring time blooms are Species Tulips

Sue

Here in a warm winter climate I do as kato b except that in September they go in a refrigerator until December when they are planted. Any bulbs less than 12cm circumference are discarded as most small than that will not bloom. Al

A friend of mine gave me some Tulips at Easter, they Died, I separated the bulbs and removed the dead "coverings"...should I try to make them grow again...or should I just let them dry and store them for later?
Annamaria

Soemone mentioned composting the small bulbs, but I was once advised to have a nursery area for planting small bulbs. When they are large enough they will bloom, and can be moved to a more showy area. I've done this with daffodils, but not tulips.

Blooming in zone 5, what is your protocol for the nursery area? Soil type? Watering? feeding? Sun/shade?

Well Tomtuxman, I don't know much about bulb care - I just wing it most of the time. For my bulb nursery I chose a sunny spot and planted the babies with plenty of space between. I never relocated them once they bagan blooming, so it's probably time to separate them. I have others that I will separate this year as well and will need to make a new nursery.
When I bought my house I found several clumps of short tulip leaves in the backyard grass. I dug, divided and replanted them and have had pretty peony tulips for several years now. My neighbors said the gardens had been neglected for many years prior, so those tulip bulbs had probably been in the ground a long time before the division and move regenerated them.
Good luck with your tulips! :)