You could do it! Lots of people do. Here are some ideas.
Tomatoes, bell peppers, hot peppers, herbs, berries, egg plants etc.
Here is a kit to start.
http://images.search.yahoo.com/search/images/view?back=http%3A%2F%2Fimages.search.yahoo.com%2Fs earch%2Fimages%3Fp%3Dindoor%2Bvegetables%26ei%3DUT F-8%26fr%3Db2ie7%26x%3Dwrt%26js%3D1%26ni%3D20&w=350& h=351&imgurl=www.healthgoods.com%2FShopping%2Fimag es%2Faerogrow_aerogarden_garden_system_black_lg.jp g&rurl=http%3A%2F%2Fwww.healthgoods.com%2FShopping %2FGardening_Products%2FAerogrow_Aerogarden_Indoor _Gardening_System.asp&size=38.2kB&name=aerogrow_ae rogarden_garden_system_black_lg.jpg&p=indoor+veget ables&type=jpeg&no=18&tt=960&oid=f87a52173db96b7a& ei=UTF-8
http://images.search.yahoo.com/search/images/view?back=http%3A%2F%2Fimages.search.yahoo.com%2Fs earch%2Fimages%3Fp%3Dloft%2Bgarden%26ei%3DUTF-8%26fr%3Db2ie7%26x%3Dwrt%26js%3D1%26ni%3D20&w=361& h=480&imgurl=static.flickr.com%2F14%2F15081228_0da 6798c9f_m.jpg&rurl=http%3A%2F%2Fwww.flickr.com%2Fp hotos%2Faltoid%2F15081228%2F&size=67.6kB&name=1508 1228_0da6798c9f.jpg&p=loft+garden&type=jpeg&no=9&t t=9,982&oid=ec35040735790d84&fusr=Altoid&tit=garde n+o%27+weeds&hurl=http%3A%2F%2Fwww.flickr.com%2Fph otos%2Faltoid%2F&ei=UTF-8&src=p
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http://images.search.yahoo.com/search/images/view?back=http%3A%2F%2Fimages.search.yahoo.com%2Fs earch%2Fimages%3Fp%3Droof%2Bvegetables%26y%3DSearc h%26ei%3DUTF-8%26fr%3Db2ie7%26x%3Dwrt%26js%3D1%26ni%3D20&w=500& h=375&imgurl=static.flickr.com%2F61%2F179776200_3f eecc35ba_m.jpg&rurl=http%3A%2F%2Fwww.flickr.com%2F photos%2Funderdutchskies%2F179776200%2F&size=207.3 kB&name=179776200_3feecc35ba.jpg&p=roof+vegetables &type=jpeg&no=5&tt=280&oid=69d0d2a9726e2a14&fusr=u nderdutchskies&tit=Growing+berries+and+vegies+on+a +roof+terrace+in+Amsterdam&hurl=http%3A%2F%2Fwww.f lickr.com%2Fphotos%2Funderdutchskies%2F&ei=UTF-8&src=p
http://www.neiu.edu/~ncaftori/benin/nati/silo-on-roof-w-vegetables.jpg
http://images.search.yahoo.com/search/images/view?back=http%3A%2F%2Fimages.search.yahoo.com%2Fs earch%2Fimages%3Fp%3Droof%2Bvegetables%26y%3DSearc h%26ei%3DUTF-8%26js%3D1%26ni%3D20%26fr%3Db2ie7%26b%3D21&w=373&h =500&imgurl=static.flickr.com%2F231%2F511003038_0e d32229f6_m.jpg&rurl=http%3A%2F%2Fwww.flickr.com%2F photos%2Fhellomuller%2F511003038%2F&size=224.4kB&n ame=511003038_0ed32229f6.jpg&p=roof+vegetables&typ e=jpeg&no=21&tt=280&oid=6a510135e51d6b12&fusr=hell oMuller&tit=Herbs&hurl=http%3A%2F%2Fwww.flickr.com %2Fphotos%2Fhellomuller%2F&ei=UTF-8&src=p
http://images.search.yahoo.com/search/images/view?back=http%3A%2F%2Fimages.search.yahoo.com%2Fs earch%2Fimages%3Fp%3Droof%2Bvegetables%26y%3DSearc h%26ei%3DUTF-8%26js%3D1%26ni%3D20%26fr%3Db2ie7%26b%3D21&w=375&h =500&imgurl=static.flickr.com%2F1085%2F1428646876_ a7c7465ed4_m.jpg&rurl=http%3A%2F%2Fwww.flickr.com% 2Fphotos%2F39141782%40N00%2F1428646876%2F&size=141 .5kB&name=1428646876_a7c7465ed4.jpg&p=roof+vegetab les&type=jpeg&no=25&tt=280&oid=df6458682fd0b920&fu sr=Mary+Loosemore&tit=One+of+Jean%27s+pepper+plant s&hurl=http%3A%2F%2Fwww.flickr.com%2Fphotos%2F3914 1782%40N00%2F&ei=UTF-8&src=p
http://www.gardeners.com/Tomato+Success+Kits/VegetableGardening_TerrificTomatoes,35-776RS,default,cp.html
http://www.gardeners.com/on/demandware.store/Sites-Gardeners-Site/default/Link-Product?sku=37-000
http://images.search.yahoo.com/search/images/view?back=http%3A%2F%2Fimages.search.yahoo.com%2Fs earch%2Fimages%3Fp%3Dindoor%2Bgardening%2Bkit%26ei %3DUTF-8%26js%3D1%26ni%3D20%26fr%3Db2ie7%26b%3D21&w=281&h =500&imgurl=www.theezgro.com%2Fimages%2Fpp%2Felite plants.jpg&rurl=http%3A%2F%2Fwww.theezgro.com%2Fel ite_home_garden.html&size=156.8kB&name=eliteplants .jpg&p=indoor+gardening+kit&type=jpeg&no=21&tt=272 &oid=aa227f0bd47ae024&ei=UTF-8
http://www.gardeninggiftguide.com/indoor%20herbs.jpg
http://www.gardeners.com/on/demandware.static/Sites-Gardeners-Site/Sites-GSC_Products/-/Products/32-707.jpg