my ex roomate is suing me for $150 over couches we bought together on craigslist. Will she win the case?

If I understand you correctly, although you admit in your question that you bought couches "together" with your former roommate, you intend to claim that the couches you took were yours, while your former roommate claims that you owned them jointly.  Whether therer was a written agreement or not is irrelevant to the issue of the validity of your former roommate's claim, although it would be easier for her to prove her case if she had a written agreement.  However, contrary to your contention, there is proof supporting her claim - your question, in which you admit that you bought the couches together.  Furthermore, I am sure that you would not commit perjury by lying about this to the Court; forgetting the moral issues, it would be incredibly stupid to risk all the consequences of a perjury conviction to save $!50.  Nevertheless, assuming that your question above doesn't come to light in the case, that you lie about buying the couches together, and that there is no evidence other than her word against yours (i.e. no other witnesses, no cancelled checks, deposit slips, check register entries or other documentation showing her payment of 1/2 the purchase price, no emails or craigslist communications in which you jointly advertised for couches, or communicated to the seller that you were purchasing the couches jointly, etc.), the issue would come down to which one of you the finder of fact (i.e. the Judge or Jury) believes.