Same word as wary:

alert, attentive, cagey, calculating, canny, chary, circumspect, considerate, discreet, distrustful, doubting, frugal, gingerly, guarded, handling with kid gloves, heedful, keeping on one's toes, leery, on guard, on the lookout, on the qui vive, provident, prudent, safe, saving, sly, sparing, suspicious, thinking twice, thrifty, unwasteful, vigilant, walking on eggs, watchful, watching one's step, watching out, wide-awake