Attack Pattern: They pop in and out of pipes at a steady rate. They won't normally come out if you are right next to the pipe, or on top of it, but the hanging ones (which don't appear in Super Mario Bros.) do come out when you're next to or under the pipe, and their are some red varieties in The Lost Levels that come out even if you're next to the pipe (they won't come out if you're on the pipe.)
Basic Fighting Strategies: If you don't have any super powers, just wait for them to go into their pipes, and then jump over (you may also be able to jump over them before they hide). If you have invicibility or fireballs (or superballs SML) you can easily kill them. A shell will also work, if you're playing Super Mario Land 2.
Advanced Fighting Strategies: It is usually possible to stand on the very edge of the pipe without hitting the Piranha Plant - so you can save some time by getting on the edge and jumping over them, if you're impatient. Also, remember that they won't normally come out if you're right next to the pipe, or on top of it, so you don't need to worry about them at those times, unless you're playing SMB:LL.

Attack Pattern: Much the same as in the last section - they pop in and out of pipes, and the regular ones won't come out if you're right next to the pipe. In this game, the hanging ones also obey this law - they'll wait if you're next to the pipe, or right under it.
Basic Fighting Strategies: Pretty much any attack other than stomping will work on them, but your best bet is fire or hammers, if you have one of those. Tail attacks are also possible, but more dangerous. Shells also work.
Advanced Strategies: As with the other games, remember that they won't come out if you're right next to them, so take advantage of that. The hanging ones might, though, so be careful around them. You can also stand on the far edge of the pipe, as I mentioned in the last section.

Attack Pattern: The hanging ones haven't changed, but the others now "jump". They are faster, and have more range than the older variety. I don't think the hanging ones will wait for you if you're next to their pipes.
Basic Fighting Strategies: Pretty much any attack other than stomping will work on them. Spin-stomping will not kill them, but it will keep you from getting hurt.
Advanced Strategies: Eating them with Yoshi will earn you a coin, which is always good. Fireballs are very effective, and will earn you a coin, plus 200 points. This is your best option.

Attack Pattern: They don't appear in pipes in this game. Instead they like to "hide" by shrinking down to a pretty small size, often around other flowers that help to hide them. Then, when unsuspecting Yoshis get near, they grow and try to eat them!
Basic Fighting Strategies: Eggs and spitting are the only effective weapon against Piranha Plants in this game. If you get eaten, you'll be stuck inside the plant while Baby Mario floats away. Press A repeatedly to get out.
Advanced Strategies: If you have six eggs, try grabbing enemies and spitting them at Piranha Plants, you'll save your eggs this way.

Attack Pattern: On the map, they act like normal Piranha Plants, only I don't think they hide when you're nearby. In battle, they use a combination of S'crow Dust (turns you into a scarecrow), Pollen Nap (puts you to sleep) and regular attacks. Regular attacks are their favourite.
Basic Fighting Strategies: It will probably take two timed hits to beat one of these guys, depending on what level you're on. Most Special attacks hardly cause any more damage than a regular one, so save your FP.
Advanced Strategies: Mallow's Thunder attack can cause enough damage to a large group of Piranhas (five) to make it worthwhile. Two timed Thunder attacks and one timed hit should take out a Piranha Plant. But stick to regular attacks for groups of one or three.
Blocking their regular attacks is fairly easy. they come up to you, and bite about three times. Press A around the end of their chomping and you'll block them. I don't think you have to be too accurate.

Attack Pattern: They're usually sleeping, but if you make a lot of noise near them, they'll wake up, and start snapping at you. They have limited range, but can be dangerous if they're in small areas, or if you're being reckless.
Basic Fighting Strategies: Your best bet is to sneak up to tip-toe up to them and punch them in the snoot while they're still sleeping (hold down less on the control stick to tip-toe.
Advanced Strategies: I think it's possible to kill a Piranha Plant by charging right up to it, and using a "kick slide" (while running, press and hold Z, then press B). This is faster than the other technique, but a little trickier, and I'm not 100% certain about it.

Attack Pattern: If I remember correctly, they basically grow out of the ground, and then they sort of sway back and forth, trying to reach you.
Basic Fighting Strategies: An egg is the only thing that will kill them, so you will want to try to avoid them whenever possible, to save ammo.

Attack Pattern: On the map, they pop in and out of the ground quickly, appearing in different places. When you enter battle, they usually use a regular attack which involves biting Mario.
Basic Fighting Strategies: It's quite difficult to run away from them on the map screen, but if you play "stop and go", dodging back and forth, you may be able to get ahead of them. Use the hammer, stomps are useless unless you have a "spiny badge" on.
Advanced Strategies: You can try to block their attacks by pressing A just as they bite down. Kooper is probably your best ally when fighting Piranha Plants, try his Dizzy Shell attack. Bombette and Lady Bow are good as well, although you won't get Bow until shortly after you've met most of the game's Piranha Plants.