SQL Server
 ODBC

 Standard Security:
"Driver={SQL Server};Server=Aron1;Database=pubs;Uid=sa;Pwd=asdasd;"

 Trusted connection:
"Driver={SQL Server};Server=Aron1;Database=pubs;Trusted_Connection=yes;"

 Prompt for username and password:
oConn.Properties("Prompt") = adPromptAlways
oConn.Open "Driver={SQL Server};Server=Aron1;DataBase=pubs;"

 OLEDB, OleDbConnection (.NET)

 Standard Security:
"Provider=sqloledb;Data Source=Aron1;Initial Catalog=pubs;User Id=sa;Password=asdasd;"

 Trusted Connection:
"Provider=sqloledb;Data Source=Aron1;Initial Catalog=pubs;Integrated Security=SSPI;"
(use serverName\instanceName as Data Source to use an specifik SQLServer instance, only SQLServer2000)
 Prompt for username and password:
oConn.Provider = "sqloledb"
oConn.Properties("Prompt") = adPromptAlways
oConn.Open "Data Source=Aron1;Initial Catalog=pubs;"

 Connect via an IP address:
"Provider=sqloledb;Data Source=190.190.200.100,1433;Network Library=DBMSSOCN;Initial Catalog=pubs;User ID=sa;Password=asdasd;"
(DBMSSOCN=TCP/IP instead of Named Pipes, at the end of the Data Source is the port to use (1433 is the default))
 SqlConnection (.NET)

 Standard Security:
"Data Source=Aron1;Initial Catalog=pubs;User Id=sa;Password=asdasd;"

 Trusted Connection:
"Data Source=Aron1;Initial Catalog=pubs;Integrated Security=SSPI;"
(use serverName\instanceName as Data Source to use an specifik SQLServer instance, only SQLServer2000)
 Connect via an IP address:
"Data Source=190.190.200.100,1433;Network Library=DBMSSOCN;Initial Catalog=pubs;User ID=sa;Password=asdasd;"
(DBMSSOCN=TCP/IP instead of Named Pipes, at the end of the Data Source is the port to use (1433 is the default))
 Declare the SqlConnection:

C#:
using System.Data.SqlClient;
SqlConnection oSQLConn = new SqlConnection();
oSQLConn.ConnectionString="my connectionstring";
oSQLConn.Open();

VB.NET:
Imports System.Data.SqlClient
Dim oSQLConn As SqlConnection = New SqlConnection()
oSQLConn.ConnectionString="my connectionstring"
oSQLConn.Open()

 Data Shape

 MS Data Shape
"Provider=MSDataShape;Data Provider=SQLOLEDB;Data Source=Aron1;Initial Catalog=pubs;User ID=sa;Password=asdasd;"

 Read more

 How to define wich network protocol to use

Example:
"Provider=sqloledb;Data Source=190.190.200.100,1433;Network Library=DBMSSOCN;Initial Catalog=pubs;User ID=sa;Password=asdasd;"

Name Network library
dbnmpntw Win32 Named Pipes
dbmssocn Win32 Winsock TCP/IP
dbmsspxn Win32 SPX/IPX
dbmsvinn Win32 Banyan Vines
dbmsrpcn Win32 Multi-Protocol (Windows RPC)

Important note!
When connecting through the SQLOLEDB provider use the syntax Network Library=dbmssocn
and when connecting through MSDASQL provider use the syntax Network=dbmssocn

 All SqlConnection connectionstring properties

This table shows all connectionstring properties for the ADO.NET SqlConnection object. Most of the properties are also used in ADO. All properties and descriptions is from msdn.

Name Default Description
Application Name   The name of the application, or '.Net SqlClient Data Provider' if no application name is provided.
AttachDBFilename
-or-
extended properties
-or-
Initial File Name   The name of the primary file, including the full path name, of an attachable database. The database name must be specified with the keyword 'database'.
Connect Timeout
-or-
Connection Timeout 15 The length of time (in seconds) to wait for a connection to the server before terminating the attempt and generating an error