Do I encode ampersands in <a href...>?

Yes, it is. HTML entities are parsed inside HTML attributes, and a stray & would create an ambiguity. That's why you should always write & instead of just & inside all HTML attributes.

That said, only & and quotes need to be encoded. If you have special characters like é in your attribute, you don't need to encode those to satisfy the HTML parser.

It used to be the case that URLs needed special treatment with non-ASCII characters, like é. You had to encode those using percent-escapes, and in this case it would give %C3%A9, because they were defined by RFC 1738. However, RFC 1738 has been superseded by RFC 3986 (URIs, Uniform Resource Identifiers) and RFC 3987 (IRIs, Internationalized Resource Identifiers), on which the WhatWG based its work to define how browsers should behave when they see an URL with non-ASCII characters in it since HTML5. It's therefore now safe to include non-ASCII characters in URLs, percent-encoded or not.

By current official HTML recommendations, the ampersand must be escaped e.g. as & in contexts like this. However, browsers do not require it, and the HTML5 CR proposes to make this a rule, so that special rules apply in attribute values. Current HTML5 validators are outdated in this respect (see bug report with comments).

It will remain possible to escape ampersands in attribute values, but apart from validation with current tools, there is no practical need to escape them in href values (and there is a small risk of making mistakes if you start escaping them).

You have two standards concerning URLs in links (<a href).

The first standard is RFC 1866 (HTML 2.0) where in "3.2.1. Data Characters" you can read the characters which need to be escaped when used as the value for an HTML attribute. (Attributes themselves do not allow special characters at all, e.g. <a hr&ef="http://... is not allowed, nor is <a hr&amp;ef="http://....)

Later this has gone into the HTML 4 standard, the characters you need to escape are:

<   to   &lt;
>   to   &gt;
&   to   &amp;
"   to   &quote;
'   to   &apos;

The other standard is RFC 3986 "Generic URI standard", where URLs are handled (this happens when the browser is about to follow a link because the user clicked on the HTML element).

reserved    = gen-delims / sub-delims

gen-delims  = ":" / "/" / "?" / "#" / "[" / "]" / "@"

sub-delims  = "!" / "$" / "&" / "'" / "(" / ")" / "*" / "+" / "," / ";" / "="

It is important to escape those characters so the client knows whether they represent data or a delimiter.

Example unescaped:

https://example.com/?user=test&password&te&st&goto=https://google.com

Example, a fully legitimate URL

https://example.com/?user=test&password&te%26st&goto=https%3A%2F%2Fgoogle.com

Example fully legitimate URL in the value of an HTML attribute:

https://example.com/?user=test&password&te%26st&goto=https%3A%2F%2Fgoogle.com

Also important scenarios:

• JavaScript code as a value:

  <img src="..." onclick="window.location.href = &quot;https://example.com/?user=test&amp;password&amp;te%26st&amp;goto=https%3A%2F%2Fgoogle.com&quot;;">...</a> (Yes, ;; is correct.)

• JSON as a value:

  <a href="..." data-analytics="{&quot;event&quot;: &quot;click&quot;}">...</a>

• Escaped things inside escaped things, double encoding, URL inside URL inside parameter, etc,...

  http://x.com/?passwordUrl=http%3A%2F%2Fy.com%2F%3Fuser%3Dtest&password=""123

_{I am posting a new answer because I find zneak's answer does not have enough examples, does not show HTML and URI handling as different aspects and standards and has some minor things missing.}