There are open source and free (as in beer) versions of vulnerability scanners. Some of which will perform similar tests to Acunetix. Some of which will only have a subset of those tests.
Many of them, however, are not bundled up as nicely and won't provide the snazzy features/interface Acunetix does. The two primary ones I can think of are Vega, which has already been mentioned, and OpenVAS. Both will perform similar types of tests against your endpoints, but neither will have that full functionality.
As Jerry Penner noted, ZAP can do some of this as well, though it requires manual configuration and supplying many of the non-generic test cases yourself. Burp PRO (which is what ZAP emulates) costs about $300 a year for a license, and is well maintained and has several built in tools that update regularly. I am a big fan of Burp and use it almost daily.