Isn't is true that in most cases, both the ss and the s-set can be interchangeable in words such as Grusse and in most cases, modern (proper German, not necessarily Bayerish German) spellings are moving more toward the ss spelling?
Note: pardon the lack of proper German characters. I'm using an English keyboard and don't want to muddy the spelling waters further by using the accepted English spelling of u-umlaut being ue.
No, if you intend on learning standard Hochdeutsch, the ß plays an important function, which is assisting with pronunciation (and therefore is of great assistance to learners of the language). ß indicates that the previous vowel is long, ss indicates the previous vowel is short. The ß does not exist in Swiss Standard German, but I don't believe spellings are moving towards ss in Hochdeutsch. If in doubt by all means use "ss" however.
Oh and just some history, ß (ess-zett), literally "sz" is a ligature, which is the merger of the letters "s" and "z". Historically there was a long "s", exactly the same as the modern mathematical integration symbol (ſ). Combined with the standard symbol for "z" in cursive script, much like a "3", you get the ß shape.
What Nachdenklich said. 'ß' and 'ss' aren't interchangeable in German and it is a spelling error if you confuse them. Since the 'Rechtschreibreform' the 'ß' is used less frequently than it was before, but apart from that I don't see any trend away from 'ß' towards 'ss'.
What the others said. You can, however, substitute the "ß" with an "ss" and the umlauts with "ue", "ae" and "oe" if you're typing on a foreign keyboard and have absolutely no possibility of using the correct characters. But this is a makeshift solution and should only be done in exceptional circumstances. (Swiss Standard German is a different matter, but that has already been explained).
Thank you all for your quick and thorough responses. Nachdenklich has some very cool historical knowledge as well.
No! Absolutely not! You can always make an esset into ss but only in very rare cases can one form two s' into an esset. In fact, in Switzerland, the esset is mostly done away with because the rules regarding it are so strict.