These toys are great for the 1-4 year old age range, depending on your child, their interests, etc. Most of these will grow with your child because they are open-ended. Some have chokables so watch out for that if you have a child under 3 or one that still mouths toys!!

Wooden building blocks - these are technically for ages 3 and older, so check for chokables before allowing your child to play with them independently.
Musical Instrument Set
- Toys with Wheels and a Tot Tube (for boys and girls!! Researchers have found that both boys and girls' play is "richer" when playing with cars than other toys.) I like these pull-back cars, these soft cars
- Items for pretend play such as play food and a grocery cartcostumesdolls and doll accessories (For boys and girls! Especially if you are thinking about having another baby...) etc
- A toy phone - great for language skills
- Games: Let's Go FishingHungry Hungry HipposZingoHedbanzGoodnight Construction SiteRoll and PlaySeek-A-Boo. Your toddler will be too young for some of these, but you can alter the rules to still have a fun family experience. 
- A play kitchen.
- A train set. I love Brio (expensive but durable - my boys still play with my husband's old set!) but there are lots of good sets out there. Just check for compatibilities with one another. (For example, Thomas fits on Brio)
- Something to practice fine motor skills such as: a pegboard setnuts and bolts playsetdesign and drill sets
- Something to practice gross motor skills such as a toddler trampolinetunnels/forts, the BilboRody, a plasma car, a scooter, the wheely bug, a collapsible balance beamRiverstones, or a balance bike
- Books!!! I love these authors/series' for kids this age: Mo Willems - Elephant and Piggy, The Llama Llama books by Anna Dewdney, David ShannonSandra Boynton books, and many more. You can never go wrong with books. :)