SPS = small polyped scleractinian coral (small
polyped stony corals)
LPS = large polyped scleractinian
Reefkeepers are often concerned about chemical warfare between corals (especially toxins from soft corals harming SPS corals), and I'm sure there is reason to think about such things. However, personally, I have always kept all sorts of corals (SPS, LPS, soft corals, gorgonians, zooanthids) in the same system, and I have not seen indications that there were any problems with this (though the relative abundances of the different corals might make a difference I suppose?...e.g. maybe it would be a bigger deal having leather corals in with SPS corals if the tank was 90% filled with leather corals rather than 10% leathers???).
I have kept LARGE amounts of Xenia in SPS tanks and have not seen any indication that the Xenia was inhibiting the SPS corals. In fact, I have seen strong indications that a large amount of Xenia can reduce problem algae growth. Also, I have not normally observed any problems from contact between Xenia and other corals, as long as the Xenia is not shading or blocking water flow from the other coral, and as long as the Xenia is not attached to the other coral. I currently have some Xenia brushing up against part of an Acropora colony – I do need to remove or trim the Xenia, but honestly, the Acropora does not seem to care.
In general though, try very hard to not allow any coral or anemone or zooanthid to touch any other coral that you care a lot about. Some can touch each other without doing any harm, but unless you know otherwise, assume that one or the other will likely be harmed by contact. The damage might be from chemical warfare, but often the damage will be from stinging.
Some corals, especially some of the LPS corals, can put out amazingly long sweeper tentacles that can sting and kill their neighbors. Galaxea and maze corals are examples that have really really long sweepers sometimes (they seem to be extended in response to neighbors that they don't like that they want to clear out of the way).
Also, some LPS corals really expand their tissues out far, even if they are not particlularly trying to be aggressive. Frogspawns, hammer, and torch corals are examples of this. These corals also grow very fast, and a small colony will occupy a huge amount of tank space before you know it. So, both because of the tremendous reach of their tentacles, and because of their fast grwoth, you need to plan and allow plenty of space around such corals.
Among SPS corals (actually, among all corals), there are hierarchies of aggression. For example, I have found that
Pocillopora damicornis (which also does the sweeper tentacle thing, but on a smaller scale) will kill Montipora digitata and birdsnest corals if they grow within range of its sweepers. Certain Acropora species seem to win out over others when they come in contact. Etc.
In general, any softy or LPS will kick SPS butt.
define sps vs lps vs softies 
