I hear it's normal to give up naps anywhere from 2-5 years of age. My son is 3-1/2 and still sleeps hard for 2 hours most days. My daughter, on the other hand, gave up naps at age 2-1/2 after having only sporadic napping habits for six months. She seemed to still really need her naps, and -on days where she didn't have one- she got really crabby in the evenings.
I had just given birth to my son and really a break in the afternoon and to have a nap myself. So instead of focusing on her sleeping, we insisted that she have some "Quiet Time" in her room, by herself, with the door shut. She didn't have to sleep, but she had to stay quiet in her room. Especially if I played soothing music, she oftentimes went to sleep on her own. Sometimes I had to remind her that Quiet Time was for quiet activities only. I also invested in some books on tape, a StoryReader, a Magnadoodle, and some other games/toys that she enjoyed playing quietly. That really seemed to make a difference for all of us. She definitely got something out of the "down" time, and we noticed a difference on the days when she didn't get even a Quiet Time. On the days where she didn't fall asleep, but she did get Quiet Time, she still was more rested and less crabby in the evenings.
Also, one trick we've used with both kids is to put their favorite toy to bed first. That way they didn't feel like they were the only ones getting put down for a nap. Sometimes we even played a little bit that their toy was being naughty, making too much noise or not wanting to lie down. Both my kids thought this was very funny, and if I told them that they were in charge of keeping kitty (or whoever) quiet during naptime, they felt like they had some control over things. At 2-1/2, getting to have some control is so important. So you might try to give your toddler some choices, like: Do you want to lie down with your kitty or your bear today? Do you want music or no music? Would you like to have a story or a back rub? (Back rubs really worked for my son, too!)
GOOD LUCK!
H.