English - Old and New - has many related languages, both near and far. The closest relatives of English are the Germanic languages, which includes the following: Frisian and Saxon (one of "Anglo-Saxon's" parent languages, hence the name); next Dutch and German; next the Scandinavian languages (Icelandic, Swedish, Danish, Norwegian, Frisian, Gutnish, and Norn) and Gothic.

Knowing Old English makes learning any of these languages considerably easier, and visa verse. For example, compare these cognate ("origin-sharing") words from some of the above named languages:

OE Ger. Dut. Got. Icel. MnE
mann mann man manna mann "man"
is ist is ist er "is"
habban haben hebben haban hafa "to have"

And the list could go on... and on...

Then there are more distant relatives of English such as Latin; Greek; the Celtic languages (such as welsh and Irish); the Slavic languages (such as Russian and Polish); more distantly, many Indian and various other Eastern languages; and many more.

The first grouping I mentioned is called the Germanic language family, and the second is called the Indo-European language family.

For further information on some of more closely related languages, try the links I've prepared below: