Ok, a few points.
If you're using myisam table, a straight select count(*) from a table is usually very fast. If you're using innodb, it has to examine the table itself and takes much longer.
Sayan, my query is likely to be more expensive than Rogers, but that depends on the database handler and size of the data set.
for an mvcc database (postgresql, mysql with innodb) select count() from sometable gets more and more expensive as the table gets larger, whereas select from sometable limit 200 has a linear performance response as the number of tuples in the table goes up.
So, this is one of those things where programming it one way (Roger's) makes MySQL fast, for myisam tables, and makes almost all other databases slow.
OTOH, programming it my way makes it middling slower than Roger's way, but it can be ported straight to oracle, firebird, postgresql, or mysql innodb with no need for a different query there.
MySQL with innodb, postgresql, and all other mvcc type databases know to shortcut a select with a limit, so my query won't be horrifically expensive. However, in databases like oracle and postgresql which can store a table in multiple files for efficiency, you should probably limit yourself to one field, not *. I.e.:
select count(*) from (select idfield from sometable limit 200) as a
if id is an integer, and a primary key, it will give you the same answer, but if the database is storing the larger text fields and such in that table in a separate file (toast tables for postgresql, partitioning for Oracle) then it will be pretty fast.