Let's take a quick sample of full-length non-children's anime that began airing during the current season (Winter 2014) and see which are based on manga.
- Based on a manga: D-Frag; Engaged to the Unidentified; Hoozuki no Reitetsu; Inari, Konkon, Koi Iroha; Maken-ki 2; Nisekoi; Nobunagun; Noragami; Saki Zenkoku-hen; Sakura Trick; Seitokai Yakuindomo 2; Silver Spoon 2; Witch Craft Works
- Based on a light novel: Chuunibyou 2; Mahou Sensou; Nourin; ImoCho; Toaru Hikuushi e no Koiuta
- Based on something else: Falcom Gakuen (a video game series); SoniAni (a mascot character)
- Not based on anything: Buddy Complex; Hamatora (simultaneous mixed-media); Nobunaga the Fool; Sekai Seifuku; Space Dandy; Wake Up, Girls!; Wizard Barristers
As we can see, roughly half of the series this season are based on a manga, and roughly half are based either on a work in some other medium or are wholly original.
To make a broader point, we can take a look at some data collected by user /u/homu on Reddit (link).
As we can see from this graph, manga has historically been the source for at least a plurality of anime adaptations (though never a majority, at least since 2000). However, other sources are by no means negligible. In particular, the rise of light novels starting circa 2005 appears to have eaten into the market share of manga adaptations, and shows no sign of slowing down as of yet.
All said and done, yes - anime that aren't based on manga are pretty common.