I am a registered massage therapist, and while I don't deal with a lot of male clients myself (most men aren't too comfortable with male therapists), I've heard some stories from my coworkers. We are taught in school that this is a natural bodily function, and any RMT worth anything will know that it's not always controllable.
Some of my coworkers have had males who become erect (although if it happens, 90% of the time it's only semi-erect), and most of them will just ignore it. The majority of the massage you will probably be lying on your stomach, and you should be fully draped with a sheet at all times, with only the body part being worked on exposed (arm, leg, torso). If you only get a towel to cover your private bits, get up and walk out, your RMT hasn't been trained properly and could possibly injure you. NEVER at any point during a massage should an RMT expose your private's, it is completely unnecessary, there isn't a body part that can't be properly draped.
If you find you have an erection when your RMT asks you to turn over onto your back, just take a minute to stretch and pretend like your too out of it to and need to regain your senses (trust me, after a while your brain enters a sort of half-sleeping, half-aware state, and it's quite common for clients to ask for a minute or two to regain their composure.)
If your lying on your back and you feel it happening, just be honest, apologize and say your not looking for that kind of massage, it's just your first time. Any professional RMT will either give you an additional towel to cover yourself with, or if they are uncomfortable, they will leave the room for a minute or two.
Rarely will an RMT freak out, if they do, they are not a professional. Be polite and apologize, but don't feel bad, they are the one who is being unreasonable.
Honestly, I wouldn't worry about it though, if you find a good RMT it won't happen, you'll be to focused on breathing through deep pressure and releasing sore muscles you didn't even know you had. Don't ask for a Swedish Massage, it has no benefit other than a few hours of relaxation. If you tell the RMT that you have some sore area's you'd like worked on (shoulders and back are always a safe bet), they will spend the time trying to release hypertonic muscles and trigger point therapy, and you will feel infinitely better.
Preferably, DO NOT go to a spa, find a clinic that performs other modalities as well, like physiotherapy, acupuncture, orthopedics, or acupressure. These health clinics will have trained, professional RMT's who have gone through extensive training about the human body. Spa's usually have massage therapists who have taken a few courses in swedish and relaxation massage, but don't have the anatomical background a health professional should.