Answer: Yes, but their usages aren't always parallel to the English usages.
In general, forms in English that require an auxiliary (other than the forms that are translated using haber) don't require auxiliaries in Spanish. A sentence in English such as "I will leave" becomes saldré in Spanish, not needing a separate word for "will." And "I am leaving" can be expressed simply as salgo.
However, the verb estar can be used as an auxiliary with the present participle, although such a usage is much less common than in English. For example, "I am leaving" can be expressed both as stated above and by saying estoy saliendo. And while it's not really an auxiliary in Spanish, the verb poder ("to be able") can be used for the English auxiliaries "can" and "may" (although there are a variety of other ways to translate "may"). For example: Puedo salir, "I can leave."
Notice similarly that infinitives (such as salir in the previous example) can follow any number of verbs. For example, you can say decidió salir ("he decided to leave"), quiero salir ("I want to leave") and pensaba salir ("I thought about leaving" or "I intended to leave"). These verbs aren't really functioning as auxiliaries; instead, the infinitives are functioning as something similar to objects.