My Preschooler Won't Go to Sleep

I have 3 toddlers that have all gone through phases of sleep resistance or anxiety of some sort. Every instance the child had a different reason for staying up. One had a bowel problem that requires medical treatment, another had started to get night terrors and was afraid to sleep and the other was just plain stubborn and wanted to test me as far as she could. You have to first figure out what is causing the behavior and then decide if the solution is medical, emotional or behavioral.
For the most part, so long as I keep my schedule up and give them a solid routine (and stick to it!), and everyone is healthy, everyone naps at the same time and goes to bed at the same time. (they are all asleep right now...and I can play on the computer!)

I feel for you , this is a tough fight I remember well.
Turns out my daughter has my insomnia,so it wasn't so much that she wouldn't sleep but that she couldn't.
Lot's to sort out before you can solve this, does he take naps, if so cut them out or move them earlier in the day.
What does he eat and drink in the few hours before bed,acid reflux kept my nephew from sleeping at that age.
Set a routine and stick to it, and tell him how important it is to sleep and let Mommy sleep. My girls know that sleep time is when they do their growing and when their bodies heal, they think that's cool. They also understand that if they don't want Mommy to be sick and grumpy they have to let me sleep , lol.
The first thing is getting him to stay in his bed quietly, we let our oldest have 2 books and one stuffed animal. In about 2 weeks she was staying in quietly and after about a month or so she was falling asleep without me going in ten times a night.
Good luck.

Do you give your 3 year old naps? When I keep my grandson, I allow him to play and when he get's tired I make sure I play with him until about 7:00 p.m. my daughter then puts both her son's in the tub which the 1 1/2 year old loves and they play some more in the tub she then washes them at about 8 p.m. and then he is ready for bed and he sleeps in the night.

Might I suggest some warm milk at night. That used to work for my oldest daughter when she wouldn't sleep. Of course she is 24 years old now.

Try to keep him up as long as you can during the day, until he adjusts to staying up all day, and sleeping all night.
If he won't sleep in his bed. Talk to him, and make him understand that this is his bed, and that is mommy's bed, and that he has to sleep in his bed. Then sit beside his bed and read to him, or play some kids music, till he falls asleep. After a while he should get used to it. Stories usually do the trick, quickly.

I've heard that tv in the evening makes kids restless. Make sure he's getting enough exercise, enough to eat and drink in the evening. Also, if you wake him up in the morning, hopefully his cycle will eventually regulate itself (ie he will finally be tired at night after being sleep deprived for awhile). Hopefully, this is just a brief phase and you will all be sleeping soundly soon!