I would venture to say no up front in terms of the table. However, the order of fields in an index and the number of fields in a WHERE matter a great deal.
Example : You have the following table :
CREATE TABLE testtable
(
a INT,
b INT,
c INT,
KEY (a,b,c)
);
Note this query :
SELECT * FROM testtable WHERE a=1 AND b=2 AND c=3;
Since every column in the WHERE clause is mentioned as a eq_ref, aka equa-reference (using =), the index can be used to zero in on one column.
Note this query :
SELECT * FROM testtable WHERE a=1 AND b>2 AND c=3;
Column a is in front of the index as an eq_ref, but Column b is not. This is a range query. Depending on the cardinality of Column a (cardinality visible in SHOW INDEXES FROM testtable), an index scan if cardinality of a=1 is very low and the total number of rows with Column a=1 is less than 5% of the number of rows in testtable, otherwise a full table scan is chosen by any Query Optimizer (MySQL, Oracle, PostgreSQL, SQL Server, etc).
Note this query :
SELECT * FROM testtable WHERE b=>2 AND c=3;
This WHERE clause never mentions Column a. Result? automatic full table scan.
As far as order of columns in a table goes, defragging tables and making table formats with fixed row lengths could reduce any possible issues with table column order is that is a suspected concern.
If anyone knows of issues with Oracle, PostgreSQL, SQL Server, or other RDBMS's concerning table column order, please chime in.