Vague question is the following:

Is there a classifcation of Lie groupoids?

Slightly less vague question is the following:

Is there a (short?) list of "types" of Lie groupoids such that any arbitrary Lie groupoid is Morita equivalent to one from the list?

Some Lie groupoids I know are the following:

1. Lie groupoids coming from manifolds $[M\rightrightarrows M]$,
2. Lie groupoids coming from Lie group $[G\rightrightarrows *]$,
3. Lie groupoids coming from action of a Lie group on a manifold $[G\times M\rightrightarrows M]$,
4. Lie groupoids coming from foliation on a manifold $\mathcal{F}(M)$,
5. Lie groupoids coming from a submersion, the submersion groupoid $[M\times_NM\rightrightarrows M]$
6. Lie groupoids coming from a principal $G$-bundle, the Gauge groupoid,
7. Lie groupoids coming from a vector bundle over $M$, the general linear Lie groupoid $[GL(E)\rightrightarrows M]$.

Do we know any "interesting" Lie groupoids that do not belong (not Morita equivalent) to the above list?

Only classification I know is if a Lie groupoid is proper and étale, then it is locally looks like action Lie groupoid.

I might have forgot one or two types, but these are the only types of Lie groupoids I have come across till now.

Vague question is the following:

Is there a classifcation of Lie groupoids?

Slightly less vague question is the following:

Is there a (short?) list of "types" of Lie groupoids such that any arbitrary Lie groupoid is Morita equivalent to one from the list?

Some Lie groupoids I know are the following:

1. Lie groupoids coming from manifolds $[M\rightrightarrows M]$,
2. Lie groupoids coming from Lie group $[G\rightrightarrows *]$,
3. Lie groupoids coming from action of a Lie group on a manifold $[G\times M\rightrightarrows M]$,
4. Lie groupoids coming from foliation on a manifold $\mathcal{F}(M)$,
5. Lie groupoids coming from a submersion, the submersion groupoid $[M\times_NM\rightrightarrows M]$
6. Lie groupoids coming from a principal $G$-bundle, the Gauge groupoid,
7. Lie groupoids coming from a vector bundle over $M$, the general linear Lie groupoid $[GL(E)\rightrightarrows M]$.

Do we know any "interesting" Lie groupoids that do not belong (not Morita equivalent) to the above list?

Only classification I know is if a Lie groupoid is proper and étale, then it is locally looks like action Lie groupoid.

I might have forgot one or two types, but these are the only types of Lie groupoids I have come across till now.

Edit: It turns out my question was not conveyed correctly. I do know that there is no hope of classifying Lie groups. I do not want to classify Lie groups. For me, all Lie groupoids that comes from Lie groups are of "same type". So, the classification I am looking for is only based on types. I think I conveyed it correctly now. If this is not clear, please do ask for more clarification.