Most commentaries render this as some sort of thorny bush (see Rashi, Ibn Ezra).
In terms of identifying which exact species it may have been, a great resource is Rabbi Kaplan's Living Torah commentary to Exodus 3:2, which states:
S'neh in Hebrew. This is most probably the black raspberry (rubus sanctusrubus sanctus), which has berries that turn red and then black (Yerushalmi, Ma'asroth 1:2, 3a; cf. Septuagint; Vulgate). The Midrash also identifies it as a species of thorn-bush (Sh'moth Rabbah 1:9, 2:9). Others identify it as the sana plant (Casia obovataCasia obovata), the shurbu (Colutea istriaColutea istria) or[or] the wild juju (Zizyphus spinaZizyphus spina).