Primarily, the range of your drivetrain affects your fastest and slowest speeds (for a given cadence).
Often there is no perfect range and selection of gearing will normally involve some compromise (Either losing top end speed or making climbs difficult).
The importance of the gear range of your drivetrain therefore varies with your usage scenario, and snobbery (@Murph!).
More front chainrings = more range, higher weight, more maintenance.
Less front chainrings = less range, lower weight, less maintenance.
Here are the options:
Front Rings Total Gear Range
4+ Now You're Just Being Silly
Total gear range is limited by chain and derailleur technology and mechanical limits. For example, it's obvious that if you have a very small to a very large cog in the cassette the chain will need to be long to accommodate the length difference as the chain goes around. The derailleur must also be able to physically move the distances involved and take up the slack in the chain. (This, incidentally, is why mountain bikes with their large range tend to have long cage derailleurs) There are limits with how different the cogs can be.
It is very difficult to judge the 'high-endianess' of a bike by the number of front sprockets. Some of the most expensive bikes I've seen have only one chainring, either for weight, maintenance or aesthetic reasons.