Chemistry - Do all salts taste salty?
Solution 1:
No. There are sweet, bitter, and various other salts. (Likely, there are tasteless salts too). Pure salty taste is as far as I know exclusive for table salt, though I wouldn't bet on it.
Lead and Beryllium salts are said to be sweet, though toxic. Epsom salt, $\ce{MgSO4}$, is bitter. $\ce{CuSO4}$ has an incomprehensible, persistent metallic taste. (Based on personal experience. Copper salts are slightly toxic, but not extremely, so I survived with no consequences.)
Salts with hydrolysing cation (various alums) are acidic in addition to other notes.
Solution 2:
Saltiness is perceived when alkali metal enter taste buds.
From wikipedia:
Saltiness is a taste produced primarily by the presence of sodium ions. Other ions of the alkali metals group also taste salty, but the further from sodium the less salty the sensation is. The size of lithium and potassium ions most closely resemble those of sodium and thus the saltiness is most similar. In contrast rubidium and cesium ions are far larger so their salty taste differs accordingly.[citation needed] The saltiness of substances is rated relative to sodium chloride (NaCl), which has an index of 1. Potassium, as potassium chloride - KCl, is the principal ingredient in salt substitutes, and has a saltiness index of 0.6. Other monovalent cations, e.g. ammonium, NH4+, and divalent cations of the alkali earth metal group of the periodic table, e.g. calcium, Ca2+, ions generally elicit a bitter rather than a salty taste even though they, too, can pass directly through ion channels in the tongue, generating an action potential.
Solution 3:
permeakra is quite right with his counterexamples of salts that don't taste purely salty, but I'd like to expand on why. We haven't fully identified and elucidated the receptors involved in taste, but they can be broadly classed into tastes people are familiar with: salty, sweet, sour, bitter, and umami.
Salty and sour receptors are both known to be mostly dominated by ion channels, where salty receptors allow small cations to pass and sour receptors are sensitive to pH in a similar fashion. The other receptors are g-protein coupled receptors. The trick with taste (and smell, for that matter) is that there is not a single receptor type for each possible chemical one can taste, i.e. there's not a receptor entirely selective towards $\ce{Na+}$. The way it works is that there are many types of taste receptors that are somewhat selective to specific classes of molecules and a given molecule may induce a response in many different receptors. The brain takes all the data from all these receptors; combines them; integrates information from the nose, eyes, ears, tactile nerves in the mouth, etc.; and then produces the sensation of taste.
Thus, though both $\ce{Na+}$ and $\ce{K+}$ will stimulate some of the same saltiness receptors, they also stimulate other receptors and in different amounts, making them taste different. In general, small cations can stimulate the ion channel receptors for saltiness, so many salts do taste salty to a certain extent, but many also stimulate other receptors. Because what we perceive as taste comes from the interaction of all these different receptors (as well as other senses), one salt may taste very salty and another quite bitter, despite both activating saltiness receptors; the responses are not independent (which is why it's possible to mask overly salty soup or whatever by adding sugar).
Solution 4:
The short answer is no, as suggested in the various comments. Not being a biologist I cannot give any underlying theory to explain this, but from personal and reported tasting I can give some examples: Copper sulphate, iron(II) sulphate, aluminium sulphate among others are very bitter. One you could try yourself would be sodium carbonate (washing soda) or sodium bicarbonate (baking soda). Interestingly Lead acetate as mentioned in one of the comments has a sweet taste which makes it particularly dangerous due to its toxicity. Even potassium chloride (used as a substitute for salt to reduce sodium intake) tastes quite different.
Solution 5:
As mentioned, while not all salts taste salty, many do, and not just salts with sodium ions. If you want to try another edible salt, try to get ahold of ammonium chloride, which is used (both as a powder and otherwise) in sweets in the Nordic countries, the Netherlands and Germany. Its taste can definitely be described as salty, but not the same kind of salty as sodium chloride.