Which are the RDBMS that minimize the server roundtrips? Which RDBMS are better (in this area) than MS SQL?

Why are you concentrating on roundtrips? Normally they shouldn't affect your performance unless you had a very slow and unreliable network. For example, the difference between ODBC and OLEDB drivers for any database is nearly an order of magnitude in favor of OLEDB.

If you go to either MySQL or Firebird using ODBC instead of OLEDB/ADO.NET drivers you incur an overhead several orders of magnituted greater than the roundtrips you might save.

How your application is coded and how and when data are accessed and transferred have a much greater impact in slow connection or high latency situations than the db network protocol itself. Some database protocols may be tuned to better work in uncommon scenarios, i.e. increasing or decreasing the data packet size.You may also encounter slow down at the TCP/IP layer itself, which could require TCP/IP tuning as well.

Until v2.1, Firebird certainly creates more traffic than MS SQL Server. I have a friend which developed a MSSQL C/S application here in Brazil where the db is hosted in a datacenter. The client apps runs from many stores directly connecting on server over VPN/Internet using end-user broadband connections (1Mbps, mostly) for 5+ years and no trouble with it. The distances involved range from few hundred to thousands of kilometers from datacenter.

After v2.1, I can't figure out if this remains true, because I haven't made a fair comparison since and Firebird's remote protocol had been changed to optimize network traffic on slow connections. More on FirebirdSQL site.

Can't say on PostGres ou MySQL, since I didn't used any.