According to "How to Grow More Vegetables" by John Jeavons, you can start almost all vegetables inside and transplant them. In my experience, this isn't necessarily true.
As @Om Patange mentions, corn, beans, and garlic are best planted straight in the ground. Potato, carrots, and parsnips (to pick some common vegetables) should also go straight in the ground.
I've had good luck transplanting the following:
- broccoli
- cabbage
- turnips*
- beets*
- squash family: zucchini, pumpkin & winter squash**, summer squash, cucumber, watermelon**
- tomato
- pepperxxx
- sunflowers
- celery
- spinach
- lettuce
- parsley
- onions
- leeks
- kale
- okraxxx
- basil
- radicchio
* I've had good luck transplanting these via soil blocks. They probably won't work when transplanted another way because of the root disturbance.
** These get big really fast. They have to go outside as soon as they germinate, or you need to start them in fairly large containers (or 4" blocks), and avoid disturbing roots when transplanting. All in all, it's probably easier to just direct seed outside.
xxx To the extent that I've had any success. They grow ok, but I never get much fruit. This isn't so much a function of transplanting, though.
Things to keep in mind when transplanting:
- Avoid disturbing roots as much as possible. Some plants are more sensitive to disturbance than others. (Especially root veg: if you disturb the roots when planting, you may get deformed roots or they may just die.)
- Soil blocks avoid root disturbance. If you're willing to make the investment in a block maker, it's a good way to get a head start on growing.
- Don't transplant at noon on a bright, sunny day. The best time to transplant is in the morning on a calm, overcast day.
- Harden off your seedlings for a week prior to transplanting. This lets them adjust from the comfortable, controlled environment indoors to the "wild west" of outdoor life.
- Water carefully for the first week or so. Note that says carefully: overwatering is just as deadly as underwatering.
- Avoid overfertilizing. If you transplant a seedling with fine roots onto a high nitrogen fertilizer, you can burn the roots. (You want fertile soil, because if you don't, they will fail to thrive. But in my experience, this shows up later in the season as weak or stunted plants and not immediate plant death.)