You might be a big dog lover, but approaching two strange dogs -- especially if they look big and intimidating -- can still be challenging. In fact, it can even be dangerous if you don't do it properly or overestimate your welcome. Don't let your fear show, though -- just move slowly and be aware of visual clues from the dogs. Their clues will tell you whether you're a welcome sight or somebody who should keep her distance.
Engage the owner first if he's present. Dogs might lunge at you or start barking if they think their owner might be in danger, so exchanging a smile and a few words with the owner before you approach the dogs might be wise. Always ask for permission to pet and whether the dogs are friendly. Ask also which dog is "the boss" -- the alpha dog -- so you can pet that one first. This will reinforce his position and prevent problems -- for you and between the dogs.
Keep your cool when approaching strange dogs, especially if the owner is not around or if they're not on a leash. Don't run, scream or make loud noises or sudden movements. Don't lock eyes with them either, as this can be interpreted as a sign of defiance. Walk slowly towards them, talking softly -- what you say matters less than your tone.
Keep your own dog under control if he's with you. Get a firm grasp on the leash and stop before you're too close -- far enough that the dogs can't touch each other. Now look at the body language of the other two dogs. Many dogs adopt "pack behavior" when they're together -- and the last thing you want is for them to gang up on your dog or you. If the doggies are wagging their tails and trying to get closer, it's probably OK. But if they're growling or the hair on their backs is getting higher, keep your distance.
Engage both dogs the same way. In short: Don't play favorites. And wait for the dogs to come towards you or wag their tails like crazy before you attempt to pet them. When you do reach out to touch them -- alpha dog first -- let them smell you first. Extend your hand and allow both dogs to become familiar with your smell. Then pet them under the chin. Don't reach over their head or touch them while they're distracted -- this can be unnerving and the dogs might bite as a surprised reaction.